University Calculus: Early Transcendentals (4th Edition)
University Calculus: Early Transcendentals (4th Edition)
4th Edition
ISBN: 9780134995540
Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Coordinate Geometry
Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …
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Chapter 11.1, Problem 68E
To determine

Prove that the point P(3, 1, 2) is equidistant from the points A(2, −1, 3) and B(4, 3, 1).

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Chapter 11 Solutions

University Calculus: Early Transcendentals (4th Edition)

Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...
Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - In Exercises 1–16, give a geometric description of...Ch. 11.1 - Prob. 16ECh. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 17–24, describe the sets of points in...Ch. 11.1 - In Exercises 25–30, find the distance between...Ch. 11.1 - In Exercises 25–30, find the distance between...Ch. 11.1 - In Exercises 25–30, find the distance between...Ch. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Find the distance from the point (3, −4, 2) to...Ch. 11.1 - Find the distance from the point (−2, 1, 4) to...Ch. 11.1 - Find the distance from the point (4, 3, 0) to...Ch. 11.1 - Find the distance from the x-axis to the plane z =...Ch. 11.1 - In Exercises 35–14, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - In Exercises 35–14, describe the given set with a...Ch. 11.1 - The set of points in space equidistant from the...Ch. 11.1 - In Exercises 35–44, describe the given set with a...Ch. 11.1 - Prob. 44ECh. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Write inequalities to describe the sets in...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find the center C and the radius a for the sphere...Ch. 11.1 - Find equations for the sphere whose centers and...Ch. 11.1 - Find equations for the sphere whose centers and...Ch. 11.1 - Prob. 63ECh. 11.1 - Prob. 64ECh. 11.1 - Find a formula for the distance from the point...Ch. 11.1 - Find a formula for the distance from the point...Ch. 11.1 - Find the perimeter of the triangle with vertices...Ch. 11.1 - Show that the point P(3, 1, 2) is equidistant from...Ch. 11.1 - Find an equation for the set of all points...Ch. 11.1 - Prob. 70ECh. 11.1 - Find the point on the sphere x2 + (y − 3)2 + (z +...Ch. 11.1 - Find the point equidistant from the points (0, 0,...Ch. 11.1 - Prob. 73ECh. 11.1 - Prob. 74ECh. 11.1 - Prob. 75ECh. 11.1 - Find all points that simultaneously lie 3 units...Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - Prob. 4ECh. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - Prob. 6ECh. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 1–8, let u = 〈3, −2〉 and v = 〈−2, 5〉....Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - In Exercises 9–16, find the component form of the...Ch. 11.2 - The unit vector that makes an angle θ = 2π/3 with...Ch. 11.2 - The unit vector that makes an angle θ = −3π/4 with...Ch. 11.2 - The unit vector obtained by rotating the vector ...Ch. 11.2 - The unit vector obtained by rotating the vector ...Ch. 11.2 - In Exercises 17–22, express each vector in the...Ch. 11.2 - Prob. 18ECh. 11.2 - In Exercises 17–22, express each vector in the...Ch. 11.2 - In Exercises 17–22, express each vector in the...Ch. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - In Exercises 23 and 24, copy vectors u, v, and w...Ch. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - In Exercises 25–30, express each vector as a...Ch. 11.2 - Prob. 30ECh. 11.2 - Find the vectors whose lengths and directions are...Ch. 11.2 - Prob. 32ECh. 11.2 - Find a vector of magnitude 7 in the direction of v...Ch. 11.2 - Prob. 34ECh. 11.2 - In Exercises 35–38, find a. the direction of and...Ch. 11.2 - In Exercises 35–38, find a. the direction of and...Ch. 11.2 - In Exercises 35–38, find a. the direction of and...Ch. 11.2 - Prob. 38ECh. 11.2 - If = i + 4j − 2k and B is the point (5, 1, 3),...Ch. 11.2 - Prob. 40ECh. 11.2 - Linear combination Let u = 2i + j, v = i + j, and...Ch. 11.2 - Linear combination Let u = i − 2j, v = 2i + 3j,...Ch. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Prob. 46ECh. 11.2 - Consider a 100-N weight suspended by two wires as...Ch. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Prob. 50ECh. 11.2 - Location A bird flies from its nest 5 km in the...Ch. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Prob. 54ECh. 11.2 - Prob. 55ECh. 11.2 - Vectors are drawn from the center of a regular...Ch. 11.2 - Prob. 57ECh. 11.2 - Prob. 58ECh. 11.2 - Consider a triangle whose vertices are A(2, –3,...Ch. 11.3 - Prob. 1ECh. 11.3 - 2. v = (3/5)i + (4/5)k, u = 5i + 12j v · u, |v|,...Ch. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - 5. v = 5j – 3k, u = i + j + k v · u, |v|, |u| the...Ch. 11.3 - Prob. 6ECh. 11.3 - v = 5i + j, v · u, | v |, | u | the cosine of the...Ch. 11.3 - v · u, | v |, | u | the cosine of the angle...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Find the angles between the vectors in Exercises...Ch. 11.3 - Prob. 13ECh. 11.3 - Rectangle Find the measures of the angles between...Ch. 11.3 - Direction angles and direction cosines The...Ch. 11.3 - Water main construction A water main is to be...Ch. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Sums and differences In the accompanying figure,...Ch. 11.3 - Prob. 20ECh. 11.3 - Diagonals of a rhombus Show that the diagonals of...Ch. 11.3 - Perpendicular diagonals Show that squares are the...Ch. 11.3 - When parallelograms are rectangles Prove that a...Ch. 11.3 - Diagonal of parallelogram Show that the indicated...Ch. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Cauchy–Schwarz inequality Since u · v = |u| |v|...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Cancelation in dot products In real-number...Ch. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Prob. 44ECh. 11.3 - Prob. 45ECh. 11.3 - Sailboat The wind passing over a boat’s sail...Ch. 11.3 - Use this fact and the results of Exercise 33 or...Ch. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Prob. 52ECh. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - Prob. 4ECh. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - Prob. 7ECh. 11.4 - In Exercises 1–8, find the length and direction...Ch. 11.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 11.4 - In Exercises 9–14, sketch the coordinate axes and...Ch. 11.4 - In Exercises 15−18, Find the area of the triangle...Ch. 11.4 - In Exercises 15−18, Find the area of the triangle...Ch. 11.4 - In Exercises 15−18, Find the area of the triangle...Ch. 11.4 - In Exercises 15−18, Find the area of the triangle...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - In Exercises 19–22, verify that (u × v) · w = (v ×...Ch. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Which of the following are always true, and which...Ch. 11.4 - Which of the following are always true, and which...Ch. 11.4 - Given nonzero vectors u, v, and w, use dot product...Ch. 11.4 - Compute (i × j) × j and i × (j × j). What can you...Ch. 11.4 - Let u, v, and w be vectors. Which of the following...Ch. 11.4 - Prob. 32ECh. 11.4 - Cancelation in cross products If u × v = u × w and...Ch. 11.4 - Double cancelation If u ≠ 0 and if u × v = u × w...Ch. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Find the areas of the parallelograms whose...Ch. 11.4 - Find the areas of the triangles whose vertices are...Ch. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Find the areas of the triangles whose vertices are...Ch. 11.4 - Prob. 46ECh. 11.4 - Find the areas of the triangles whose vertices are...Ch. 11.4 - Find the volume of a parallelepiped with one of...Ch. 11.4 - Triangle area Find a 2 × 2 determinant formula for...Ch. 11.4 - Triangle area Find a concise 3 × 3 determinant...Ch. 11.4 - Using the methods of Section 6.1, where volume is...Ch. 11.4 - Prob. 52ECh. 11.4 - Using the methods of Section 6.1, where volume is...Ch. 11.4 - Using the methods of Section 6.1, where volume is...Ch. 11.4 - In Exercises 55–57, determine whether the given...Ch. 11.4 - Prob. 56ECh. 11.4 - Prob. 57ECh. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Prob. 7ECh. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Find parametric equations for the lines in...Ch. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Prob. 14ECh. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Prob. 16ECh. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Find parametrizations for the line segments...Ch. 11.5 - Prob. 20ECh. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Planes Find equations for the planes in Exercises...Ch. 11.5 - Planes Find equations for the planes in Exercises...Ch. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Find equations for the planes in Exercises...Ch. 11.5 - Prob. 27ECh. 11.5 - Prob. 28ECh. 11.5 - In Exercises 29 and 30, find the plane containing...Ch. 11.5 - In Exercises 29 and 30, find the plane containing...Ch. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - In Exercises 33–38, find the distance from the...Ch. 11.5 - Prob. 37ECh. 11.5 - Prob. 38ECh. 11.5 - In Exercises 39–44, find the distance from the...Ch. 11.5 - In Exercises 39–44, find the distance from the...Ch. 11.5 - In Exercises 39–44, find the distance from the...Ch. 11.5 - In Exercises 39−44, find the distance from the...Ch. 11.5 - Prob. 43ECh. 11.5 - Prob. 44ECh. 11.5 - Find the distance from the plane x + 2y + 6z = 1...Ch. 11.5 - Find the distance from the line x = 2 + t, y = 1 +...Ch. 11.5 - Find the angles between the planes in Exercises 47...Ch. 11.5 - Prob. 48ECh. 11.5 - Find the acute angles between the intersecting...Ch. 11.5 - Prob. 50ECh. 11.5 - Find the acute angles between the lines and planes...Ch. 11.5 - Prob. 52ECh. 11.5 - Prob. 53ECh. 11.5 - Prob. 54ECh. 11.5 - Prob. 55ECh. 11.5 - Prob. 56ECh. 11.5 - In Exercises 57–60, find the point in which the...Ch. 11.5 - In Exercises 57–60, find the point in which the...Ch. 11.5 - In Exercises 57–60, find the point in which the...Ch. 11.5 - Prob. 60ECh. 11.5 - Find parametrizations for the lines in which the...Ch. 11.5 - Prob. 62ECh. 11.5 - Prob. 63ECh. 11.5 - Prob. 64ECh. 11.5 - Given two lines in space, either they are...Ch. 11.5 - Given two lines in space, either they are...Ch. 11.5 - Use Equations (3) to generate a parametrization of...Ch. 11.5 - Use the component form to generate an equation for...Ch. 11.5 - Find the points in which the line x = 1 + 2t, y =...Ch. 11.5 - Find equations for the line in the plane z = 3...Ch. 11.5 - Prob. 71ECh. 11.5 - How can you tell when two planes A1x + B1y + C1z =...Ch. 11.5 - Find two different planes whose intersection is...Ch. 11.5 - Find a plane through the origin that is...Ch. 11.5 - The graph of is a plane for any nonzero numbers...Ch. 11.5 - Prob. 76ECh. 11.5 - Prob. 77ECh. 11.5 - Prob. 78ECh. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - In Exercises 1–12, match the equation with the...Ch. 11.6 - Drawing Sketch the surfaces in Exercises...Ch. 11.6 - Drawing Sketch the surfaces in Exercises...Ch. 11.6 - Drawing Sketch the surfaces in Exercises...Ch. 11.6 - Drawing Sketch the surfaces in Exercises...Ch. 11.6 - Drawing Sketch the surfaces in Exercises...Ch. 11.6 - Drawing Sketch the surfaces in Exercises...Ch. 11.6 - Drawing Sketch the surfaces in Exercises...Ch. 11.6 - Drawing Sketch the surfaces in Exercises...Ch. 11.6 - Drawing Sketch the surfaces in Exercises 13–44. Ch. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - Drawing Sketch the surfaces in Exercises 13–44. Ch. 11.6 - Prob. 26ECh. 11.6 - Prob. 27ECh. 11.6 - Prob. 28ECh. 11.6 - Drawing Sketch the surfaces in Exercises...Ch. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Prob. 33ECh. 11.6 - Prob. 34ECh. 11.6 - Prob. 35ECh. 11.6 - Prob. 36ECh. 11.6 - Prob. 37ECh. 11.6 - Prob. 38ECh. 11.6 - Prob. 39ECh. 11.6 - Prob. 40ECh. 11.6 - Prob. 41ECh. 11.6 - Prob. 42ECh. 11.6 - Prob. 43ECh. 11.6 - Prob. 44ECh. 11.6 - Express the area A of the cross-section cut from...Ch. 11.6 - Prob. 46ECh. 11.6 - Prob. 47ECh. 11.6 - Prob. 48ECh. 11.6 - Prob. 49ECh. 11.6 - Prob. 50ECh. 11.6 - Prob. 51ECh. 11.6 - Prob. 52ECh. 11 - Prob. 1GYRCh. 11 - How are vectors added and subtracted...Ch. 11 - Prob. 3GYRCh. 11 - Prob. 4GYRCh. 11 - Define the dot product (scalar product) of two...Ch. 11 - Prob. 6GYRCh. 11 - Prob. 7GYRCh. 11 - Prob. 8GYRCh. 11 - Prob. 9GYRCh. 11 - Prob. 10GYRCh. 11 - Prob. 11GYRCh. 11 - Prob. 12GYRCh. 11 - What are box products? What significance do they...Ch. 11 - Prob. 14GYRCh. 11 - Prob. 15GYRCh. 11 - Prob. 16GYRCh. 11 - Prob. 17GYRCh. 11 - In Exercises 1–4, let u = ⟨−3, 4⟩ and v = ⟨2, −5⟩....Ch. 11 - Prob. 2PECh. 11 - Prob. 3PECh. 11 - Prob. 4PECh. 11 - Prob. 5PECh. 11 - In Exercises 5-8, find the component form of the...Ch. 11 - The vector 2 units long in the direction 4i − j Ch. 11 - The vector 5 units long in the direction opposite...Ch. 11 - Express the vectors in Exercises 9–12 in terms of...Ch. 11 - Prob. 10PECh. 11 - Prob. 11PECh. 11 - Prob. 12PECh. 11 - Prob. 13PECh. 11 - Prob. 14PECh. 11 - Prob. 15PECh. 11 - Prob. 16PECh. 11 - In Exercises 17 and 18, find |v|, |u|, , the angle...Ch. 11 - Prob. 18PECh. 11 - In Exercises 19 and 20, find projv u. v = 2i + j −...Ch. 11 - Prob. 20PECh. 11 - In Exercises 21 and 22, draw coordinate axes and...Ch. 11 - Prob. 22PECh. 11 - Prob. 23PECh. 11 - Prob. 24PECh. 11 - In Exercises 25 and 26, find (a) the area of the...Ch. 11 - Prob. 26PECh. 11 - Suppose that n is normal to a plane and that v is...Ch. 11 - Find a vector in the plane parallel to the line ax...Ch. 11 - In Exercises 29 and 30, find the distance from the...Ch. 11 - Prob. 30PECh. 11 - Prob. 31PECh. 11 - Parametrize the line segment joining the points...Ch. 11 - In Exercises 33 and 34, find the distance from the...Ch. 11 - Prob. 34PECh. 11 - Prob. 35PECh. 11 - Prob. 36PECh. 11 - In Exercises 37 and 38, find an equation for the...Ch. 11 - Prob. 38PECh. 11 - Prob. 39PECh. 11 - Prob. 40PECh. 11 - Find the acute angle between the planes x = 7 and...Ch. 11 - Prob. 42PECh. 11 - Find parametric equations for the line in which...Ch. 11 - Prob. 44PECh. 11 - Prob. 45PECh. 11 - Prob. 46PECh. 11 - Prob. 47PECh. 11 - Prob. 48PECh. 11 - Prob. 49PECh. 11 - Prob. 50PECh. 11 - Prob. 51PECh. 11 - Prob. 52PECh. 11 - Prob. 53PECh. 11 - Prob. 54PECh. 11 - Find the point in which the line through P(3, 2,...Ch. 11 - Prob. 56PECh. 11 - Prob. 57PECh. 11 - Prob. 58PECh. 11 - Prob. 59PECh. 11 - Is the line related in any way to the plane ?...Ch. 11 - Which of the following are equations for the plane...Ch. 11 - The parallelogram shown here has vertices at A(2,...Ch. 11 - Prob. 63PECh. 11 - Prob. 64PECh. 11 - Prob. 65PECh. 11 - Prob. 66PECh. 11 - Prob. 67PECh. 11 - Prob. 68PECh. 11 - Prob. 69PECh. 11 - Prob. 70PECh. 11 - Prob. 71PECh. 11 - Prob. 72PECh. 11 - Prob. 73PECh. 11 - Prob. 74PECh. 11 - Prob. 75PECh. 11 - Prob. 76PECh. 11 - Prob. 1AAECh. 11 - Prob. 2AAECh. 11 - Prob. 3AAECh. 11 - Prob. 4AAECh. 11 - Prob. 5AAECh. 11 - Prob. 6AAECh. 11 - Prob. 7AAECh. 11 - Prob. 8AAECh. 11 - Prob. 9AAECh. 11 - Prob. 10AAECh. 11 - Prob. 11AAECh. 11 - Prob. 12AAECh. 11 - Prob. 13AAECh. 11 - Prob. 14AAECh. 11 - Prob. 15AAECh. 11 - Prob. 16AAECh. 11 - Prob. 17AAECh. 11 - Prob. 18AAECh. 11 - Prob. 19AAECh. 11 - By forming the cross product of two appropriate...Ch. 11 - Prob. 21AAECh. 11 - Prob. 22AAECh. 11 - Prob. 23AAECh. 11 - Prob. 24AAECh. 11 - Prob. 25AAE
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03 - The Cartesian coordinate system; Author: Technion;https://www.youtube.com/watch?v=hOgKEplCx5E;License: Standard YouTube License, CC-BY
What is the Cartesian Coordinate System? | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=mgx0kT5UbKk;License: Standard YouTube License, CC-BY