EBK THOMAS' CALCULUS
14th Edition
ISBN: 9780134654874
Author: WEIR
Publisher: VST
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Chapter 12.2, Problem 55E
To determine
Prove that the two segments joining the midpoints of opposite sides of ABCD bisect each other.
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Chapter 12 Solutions
EBK THOMAS' CALCULUS
Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...
Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - Prob. 12ECh. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - In Exercises 1–16, give a geometric description of...Ch. 12.1 - Prob. 16ECh. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 17–24, describe the sets of points in...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - In Exercises 25–30, find the distance between...Ch. 12.1 - Find the distance from the point (3, −4, 2) to...Ch. 12.1 - Find the distance from the point (−2, 1, 4) to...Ch. 12.1 - Find the distance from the point (4, 3, 0) to...Ch. 12.1 - Find the distance from the
x-axis to the plane z =...Ch. 12.1 - In Exercises 35–14, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - Prob. 38ECh. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–14, describe the given set with a...Ch. 12.1 - The set of points in space equidistant from the...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - In Exercises 35–44, describe the given set with a...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Write inequalities to describe the sets in...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find the center C and the radius a for the sphere...Ch. 12.1 - Find equations for the sphere whose centers and...Ch. 12.1 - Find equations for the sphere whose centers and...Ch. 12.1 - Find equations for the sphere whose centers and...Ch. 12.1 - Prob. 64ECh. 12.1 - Find a formula for the distance from the point...Ch. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 69ECh. 12.1 - Find an equation for the set of all points...Ch. 12.1 - Find the point on the sphere x2 + (y − 3)2 + (z +...Ch. 12.1 - Prob. 72ECh. 12.1 - Find an equation for the set of points equidistant...Ch. 12.1 - Find an equation for the set of points equidistant...Ch. 12.1 - Find an equation for the set of points equidistant...Ch. 12.1 - Find all points that simultaneously lie 3 units...Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - Prob. 6ECh. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 12.2 - In Exercises 9–16, find the component form of the...Ch. 12.2 - In Exercises 9–16, find the component form of the...Ch. 12.2 - In Exercises 9–16, find the component form of the...Ch. 12.2 - In Exercises 9–16, find the component form of the...Ch. 12.2 - The unit vector that makes an angle θ = 2π/3 with...Ch. 12.2 - The unit vector that makes an angle θ = −3π/4 with...Ch. 12.2 - The unit vector obtained by rotating the vector ...Ch. 12.2 - The unit vector obtained by rotating the vector ...Ch. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - In Exercises 17–22, express each vector in the...Ch. 12.2 - Prob. 22ECh. 12.2 - In Exercises 23 and 24, copy vectors u, v, and w...Ch. 12.2 - In Exercises 23 and 24, copy vectors u, v, and w...Ch. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - In Exercises 25–30, express each vector as a...Ch. 12.2 - In Exercises 25–30, express each vector as a...Ch. 12.2 - Find the vectors whose lengths and directions are...Ch. 12.2 - Find the vectors whose lengths and directions are...Ch. 12.2 - Find a vector of magnitude 7 in the direction of v...Ch. 12.2 - Prob. 34ECh. 12.2 - In Exercises 35–38, find a. the direction of and...Ch. 12.2 - Prob. 36ECh. 12.2 - In Exercises 35–38, find a. the direction of and...Ch. 12.2 - In Exercises 35–38, find a. the direction of and...Ch. 12.2 - If = i + 4j − 2k and B is the point (5, 1, 3),...Ch. 12.2 - If = −7i + 3j + 8k and A is the point (−2, −3,...Ch. 12.2 - Linear combination Let u = 2i + j, v = i + j, and...Ch. 12.2 - Prob. 42ECh. 12.2 - Linear combination Let u = ⟨ 1, 2, 1 ⟩, v = ⟨ 1,...Ch. 12.2 - Linear combination Let u = ⟨1, 2, 2 ⟩, v = ⟨ 1,...Ch. 12.2 - Velocity An airplane is flying in the direction...Ch. 12.2 - (Continuation of Example 8.) What speed and...Ch. 12.2 - Prob. 47ECh. 12.2 - Consider a 50-N weight suspended by two wires as...Ch. 12.2 - Consider a w-N weight suspended by two wires as...Ch. 12.2 - Consider a 25-N weight suspended by two wires as...Ch. 12.2 - Location A bird flies from its nest 5 km in the...Ch. 12.2 - Use similar triangles to find the coordinates of...Ch. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Let ABCD be a general, not necessarily planar,...Ch. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.3 - Prob. 1ECh. 12.3 - 2. v = (3/5)i + (4/5)k, u = 5i + 12j
v · u, |v|,...Ch. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - 5. v = 5j – 3k, u = i + j + k
v · u, |v|, |u|
the...Ch. 12.3 - Prob. 6ECh. 12.3 - v = 5i + j,
v · u, | v |, | u |
the cosine of the...Ch. 12.3 -
v · u, | v |, | u |
the cosine of the angle...Ch. 12.3 - Find the angles between the vectors in Exercises...Ch. 12.3 - Find the angles between the vectors in Exercises...Ch. 12.3 - Find the angles between the vectors in Exercises...Ch. 12.3 - Find the angles between the vectors in Exercises...Ch. 12.3 - Prob. 13ECh. 12.3 - Rectangle Find the measures of the angles between...Ch. 12.3 - Direction angles and direction cosines The...Ch. 12.3 - Water main construction A water main is to be...Ch. 12.3 - For Exercises 17 and 18, find the acute angle...Ch. 12.3 - For Exercises 17 and 18, find the acute angle...Ch. 12.3 - Sums and differences In the accompanying figure,...Ch. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Perpendicular diagonals Show that squares are the...Ch. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Cauchy–Schwarz inequality Since u · v = |u| |v|...Ch. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Cancelation in dot products In real-number...Ch. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Locomotive The Union Pacific’s Big Boy locomotive...Ch. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 -
Use this fact and the results of Exercise 33 or...Ch. 12.3 -
Use this fact and the results of Exercise 33 or...Ch. 12.3 - Prob. 49ECh. 12.3 - Prob. 50ECh. 12.3 - Prob. 51ECh. 12.3 - Prob. 52ECh. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 1–8, find the length and direction...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 15−18,
Find the area of the triangle...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - In Exercises 25 and 26, find the magnitude of the...Ch. 12.4 - In Exercises 25 and 26, find the magnitude of the...Ch. 12.4 - Which of the following are always true, and which...Ch. 12.4 - Which of the following are always true, and which...Ch. 12.4 - Given nonzero vectors u, v, and w, use dot product...Ch. 12.4 - Compute (i × j) × j and i × (j × j). What can you...Ch. 12.4 - Let u, v, and w be vectors. Which of the following...Ch. 12.4 - Prob. 32ECh. 12.4 - Prob. 33ECh. 12.4 - Double cancelation If u ≠ 0 and if u × v = u × w...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the parallelograms whose...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Prob. 44ECh. 12.4 - Prob. 45ECh. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the areas of the triangles whose vertices are...Ch. 12.4 - Find the volume of a parallelepiped with one of...Ch. 12.4 - Triangle area Find a 2 × 2 determinant formula for...Ch. 12.4 - Prob. 50ECh. 12.4 - Using the methods of Section 6.1, where volume is...Ch. 12.4 - Prob. 52ECh. 12.4 - Prob. 53ECh. 12.4 - Prob. 54ECh. 12.4 - Prob. 55ECh. 12.4 - Prob. 56ECh. 12.4 - Prob. 57ECh. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Prob. 7ECh. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Find parametric equations for the lines in...Ch. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Prob. 17ECh. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find parametrizations for the line segments...Ch. 12.5 - Find equations for the planes in Exercises...Ch. 12.5 - Find equations for the planes in Exercises...Ch. 12.5 - Planes
Find equations for the planes in Exercises...Ch. 12.5 - Planes
Find equations for the planes in Exercises...Ch. 12.5 - Find equations for the planes in Exercises...Ch. 12.5 - Find equations for the planes in Exercises...Ch. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - In Exercises 29 and 30, find the plane containing...Ch. 12.5 - Prob. 30ECh. 12.5 - Find a plane through P0(2, 1, –1) and...Ch. 12.5 - Find a plane through the points P1(1, 2, 3), P2(3,...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 33–38, find the distance from the...Ch. 12.5 - In Exercises 39–44, find the distance from the...Ch. 12.5 - In Exercises 39–44, find the distance from the...Ch. 12.5 - In Exercises 39–44, find the distance from the...Ch. 12.5 - In Exercises 39−44, find the distance from the...Ch. 12.5 - In Exercises 39−44, find the distance from the...Ch. 12.5 - In Exercises 39−44, find the distance from the...Ch. 12.5 - Find the distance from the plane x + 2y + 6z = 1...Ch. 12.5 - Find the distance from the line x = 2 + t, y = 1 +...Ch. 12.5 - Find the angles between the planes in Exercises 47...Ch. 12.5 - Find the angles between the planes in Exercises 47...Ch. 12.5 - Prob. 49ECh. 12.5 - Prob. 50ECh. 12.5 - Prob. 51ECh. 12.5 - Prob. 52ECh. 12.5 - Prob. 53ECh. 12.5 - Use a calculator to find the acute angles between...Ch. 12.5 - Prob. 55ECh. 12.5 - Use a calculator to find the acute angles between...Ch. 12.5 - In Exercises 57–60, find the point in which the...Ch. 12.5 - In Exercises 57–60, find the point in which the...Ch. 12.5 - In Exercises 57–60, find the point in which the...Ch. 12.5 - Prob. 60ECh. 12.5 - Prob. 61ECh. 12.5 - Find parametrizations for the lines in which the...Ch. 12.5 - Prob. 63ECh. 12.5 - Prob. 64ECh. 12.5 - Given two lines in space, either they are...Ch. 12.5 - Given two lines in space, either they are...Ch. 12.5 - Use Equations (3) to generate a parametrization of...Ch. 12.5 - Prob. 68ECh. 12.5 - Prob. 69ECh. 12.5 - Prob. 70ECh. 12.5 - Is the line x = 1 − 2t, y = 2 + 5t, z = −3t...Ch. 12.5 - Prob. 72ECh. 12.5 - Prob. 73ECh. 12.5 - Prob. 74ECh. 12.5 - Prob. 75ECh. 12.5 - Prob. 76ECh. 12.5 - Prob. 77ECh. 12.5 - Hidden lines in computer graphics Here is another...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - In Exercises 1–12, match the equation with the...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises 13–44.
Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises 13-44.
x2...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Drawing
Sketch the surfaces in Exercises...Ch. 12.6 - Sketch the surfaces in Exercises 13−44.
39. x2 +...Ch. 12.6 - Prob. 40ECh. 12.6 - Sketch the surfaces in Exercises 13−44.
41. z =...Ch. 12.6 - Prob. 42ECh. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.6 - Express the area A of the cross-section cut from...Ch. 12.6 - The barrel shown here is shaped like an ellipsoid...Ch. 12.6 - Prob. 47ECh. 12.6 - Prob. 48ECh. 12.6 - Prob. 49ECh. 12.6 - Prob. 50ECh. 12.6 - Prob. 51ECh. 12.6 - Prob. 52ECh. 12 - Prob. 1GYRCh. 12 - How are vectors added and subtracted...Ch. 12 - Prob. 3GYRCh. 12 - Prob. 4GYRCh. 12 - Prob. 5GYRCh. 12 - Prob. 6GYRCh. 12 - Prob. 7GYRCh. 12 - Prob. 8GYRCh. 12 - What geometric or physical interpretations do...Ch. 12 - Prob. 10GYRCh. 12 - Prob. 11GYRCh. 12 - Prob. 12GYRCh. 12 - Prob. 13GYRCh. 12 - Prob. 14GYRCh. 12 - Prob. 15GYRCh. 12 - Prob. 16GYRCh. 12 - Prob. 17GYRCh. 12 - Prob. 1PECh. 12 - Prob. 2PECh. 12 - Prob. 3PECh. 12 - Prob. 4PECh. 12 - Prob. 5PECh. 12 - Prob. 6PECh. 12 - Prob. 7PECh. 12 - The vector 5 units long in the direction opposite...Ch. 12 - Express the vectors in Exercises 9–12 in terms of...Ch. 12 - Prob. 10PECh. 12 - Prob. 11PECh. 12 - Prob. 12PECh. 12 - Prob. 13PECh. 12 - Prob. 14PECh. 12 - Prob. 15PECh. 12 - Prob. 16PECh. 12 - In Exercises 17 and 18, find |v|, |u|, , the angle...Ch. 12 - In Exercises 17 and 18, find |v|, |u|, , the angle...Ch. 12 - Prob. 19PECh. 12 - In Exercises 19 and 20, find projv u.
u = i − 2j
v...Ch. 12 - Prob. 21PECh. 12 - Prob. 22PECh. 12 - Prob. 23PECh. 12 - For what value or values of a will the vectors u =...Ch. 12 - In Exercises 25 and 26, find (a) the area of the...Ch. 12 - Prob. 26PECh. 12 - Suppose that n is normal to a plane and that v is...Ch. 12 - Find a vector in the plane parallel to the line ax...Ch. 12 - In Exercises 29 and 30, find the distance from the...Ch. 12 - Prob. 30PECh. 12 - Prob. 31PECh. 12 - Parametrize the line segment joining the points...Ch. 12 - In Exercises 33 and 34, find the distance from the...Ch. 12 - In Exercises 33 and 34, find the distance from the...Ch. 12 - Prob. 35PECh. 12 - Find an equation for the plane that passes through...Ch. 12 - In Exercises 37 and 38, find an equation for the...Ch. 12 - Prob. 38PECh. 12 - Prob. 39PECh. 12 - Prob. 40PECh. 12 - Prob. 41PECh. 12 - Prob. 42PECh. 12 - Prob. 43PECh. 12 - Show that the line in which the planes
x + 2y −...Ch. 12 - The planes 3x + 6z = 1 and 2x + 2y − z = 3...Ch. 12 - Find an equation for the plane that passes through...Ch. 12 - Prob. 47PECh. 12 - Prob. 48PECh. 12 - Find the distance from the point P(1, 4, 0) to the...Ch. 12 - Find the distance from the point (2, 2, 3) to the...Ch. 12 - Find a vector parallel to the plane 2x − y − z = 4...Ch. 12 - Prob. 52PECh. 12 - Prob. 53PECh. 12 - Prob. 54PECh. 12 - Prob. 55PECh. 12 - Prob. 56PECh. 12 - The line
intersects the plane x + 3y − z = −4...Ch. 12 - Show that for every real number k, the...Ch. 12 - Prob. 59PECh. 12 - Is the line related in any way to the plane ?...Ch. 12 - Prob. 61PECh. 12 - The parallelogram shown here has vertices at A(2,...Ch. 12 - Prob. 63PECh. 12 - Prob. 64PECh. 12 - Prob. 65PECh. 12 - Prob. 66PECh. 12 - Prob. 67PECh. 12 - Prob. 68PECh. 12 - Prob. 69PECh. 12 - Prob. 70PECh. 12 - Prob. 71PECh. 12 - Prob. 72PECh. 12 - Prob. 73PECh. 12 - Prob. 74PECh. 12 - Prob. 75PECh. 12 - Prob. 76PECh. 12 - Prob. 1AAECh. 12 - Prob. 2AAECh. 12 - Prob. 3AAECh. 12 - Prob. 4AAECh. 12 - Prob. 5AAECh. 12 - Prob. 6AAECh. 12 - Prob. 7AAECh. 12 - Prob. 8AAECh. 12 - Consider a regular tetrahedron of side length...Ch. 12 - Prob. 10AAECh. 12 - Prob. 11AAECh. 12 - Use vectors to show that the distance from to the...Ch. 12 - Prob. 13AAECh. 12 - Prob. 14AAECh. 12 - The projection of a vector on a plane Let P be a...Ch. 12 - The accompanying figure shows nonzero vectors v,...Ch. 12 - Prob. 17AAECh. 12 - Prob. 18AAECh. 12 - Prob. 19AAECh. 12 - Prob. 20AAECh. 12 - Prob. 21AAECh. 12 - Prob. 22AAECh. 12 - Prob. 23AAECh. 12 - Prob. 24AAECh. 12 - Prob. 25AAE
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- An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane? 428 mph 41° 50 mph a. The ground speed of the airplane is b. The bearing of the airplane is mph. south of west.arrow_forwardRylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude and its direction angle from the positive x-axis. 119 lb 20.2° 377 lb a. The resultant force is (Tip: omit degree notations from your answers; e.g. enter cos(45) instead of cos(45°)) b. It's magnitude is lb. c. It's angle from the positive x-axis isarrow_forwardFind a plane containing the point (3, -3, 1) and the line of intersection of the planes 2x + 3y - 3z = 14 and -3x - y + z = −21. The equation of the plane is:arrow_forward
- Determine whether the lines L₁ : F(t) = (−2, 3, −1)t + (0,2,-3) and L2 : ƒ(s) = (2, −3, 1)s + (−10, 17, -8) intersect. If they do, find the point of intersection. ● They intersect at the point They are skew lines They are parallel or equalarrow_forwardAnswer questions 2arrow_forwardHow does a fourier transform works?arrow_forward
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- There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three investment? STEP 1: The formula for compound interest is A = nt = P(1 + − − ) n², where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to A = Pert Find r and n for each model, and use these values to write A in terms of t for each case. Annual Model r=0.10 A = Y(t) = 1150 (1.10)* n = 1 Quarterly Model r = 0.10 n = 4 A = Q(t) = 1150(1.025) 4t Continuous Model r=0.10 A = C(t) =…arrow_forwardUse a graphing utility to find the point of intersection, if any, of the graphs of the functions. Round your result to three decimal places. (Enter NONE in any unused answer blanks.) y = 100e0.01x (x, y) = y = 11,250 ×arrow_forward5. For the function y-x³-3x²-1, use derivatives to: (a) determine the intervals of increase and decrease. (b) determine the local (relative) maxima and minima. (e) determine the intervals of concavity. (d) determine the points of inflection. (e) sketch the graph with the above information indicated on the graph.arrow_forward
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