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Math
Calculus
Calculus, Early Transcendentals
Chapter 12.2, Problem 4DP
Chapter 12.2, Problem 4DP
BUY
Calculus, Early Transcendentals
9th Edition
ISBN:
9781337613927
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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12.1 Three-dimensional Coordinate Systems
12.2 Vectors
12.3 The Dot Product
12.4 The Cross Product
12.5 Equations Of Lines And Planes
12.6 Cylinders And Quadric Surfaces
Chapter Questions
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Problem 1E
Problem 2E: What is the relationship between the point (4, 7) and the vector 4,7 ? Illustrate with a sketch.
Problem 3E: Name all the equal vectors in the parallelogram shown.
Problem 4E: Using the vectors shown in the figure, write each sum or difference as a single vector. (a) AB+BC...
Problem 5E: Copy the vectors in the figure and use them to draw the following vectors. (a) a+b (b) b+c (c) a+c...
Problem 6E
Problem 7E: In the figure, the tip of c and the tail of d are both the midpoint of QR. Express c and d in terms...
Problem 8E: If the vectors in the figure satisfy |u | = | v | = 1 and u + v + w = 0, what is | w |?
Problem 9E: Find a vector a with representation given by the directed line segment AB. Draw AB and the...
Problem 10E: Find a vector a with representation given by the directed line segment AB. Draw AB and the...
Problem 11E: Find a vector a with representation given by the directed line segment AB. Draw AB and the...
Problem 12E: Find a vector a with representation given by the directed line segment AB. Draw AB and the...
Problem 13E: Find a vector a with representation given by the directed line segment AB . Draw AB and the...
Problem 14E
Problem 15E: Find the sum of the given vectors and illustrate geometrically. 15. 1, 4, 6, 2
Problem 16E: Find the sum of the given vectors and illustrate geometrically. 16. 3, 1, 1, 5
Problem 17E: Find the sum of the given vectors and illustrate geometrically. 17. 3, 0, 1, 0, 8, 0
Problem 18E: Find the sum of the given vectors and illustrate geometrically. 18. 1, 3, 2, 0, 0, 6
Problem 19E: Find a + b, 4a + 2b, | a |, and | a b | 19. a = 3, 4, b = 9, 1
Problem 20E: Find a + b, 4a + 2b, | a |, and | a b | 20. a = 5i + 3j, b = i 2j
Problem 21E: Find a + b, 4a + 2b, | a |, and | a b | 21. a = 4i 3j + 2k, b = 2i 4k
Problem 22E: Find a + b, 4a + 2b, | a |, and | a b | 22. a = 8, 1, 4, b = 5, 2, 1
Problem 23E: Find a unit vector that has the same direction as the given vector. 23. 6, 2
Problem 24E
Problem 25E: Find a unit vector that has the same direction as the given vector. 25. 8i j + 4k
Problem 26E: Find the vector that has the same direction as 6, 2, 3 but has length 4.
Problem 27E
Problem 28E
Problem 29E: The initial point of a vector v in V2 is the origin and the terminal point is in quadrant II. If v...
Problem 30E
Problem 31E
Problem 32E: Find the magnitude of the resultant force and the angle it makes with the positive x-axis. 33.
Problem 33E: Find the magnitude of the resultant force and the angle it makes with the positive x-axis. 33.
Problem 34E
Problem 35E: A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. The...
Problem 36E: The tension vector at each end of a chain has magnitude 25N (see the figure). What is the weight of...
Problem 37E: Three forces act on an object. Two of the forces are at an angle of 100 to each other and have...
Problem 38E
Problem 39E
Problem 40E: A ship is sailing west at a speed of 32km/h and a dog is running due north on the deck of the ship...
Problem 41E: Find the unit vectors that are parallel to the tangent line to the parabola y = x2 at the point (2,...
Problem 42E
Problem 43E: If A, B, and C are the vertices of a triangle, find AB+BC+CA
Problem 44E: Let C be the point on the line segment AB that is twice as far from B as it is from A. If a = OA, b...
Problem 45E: (a) Draw the vectors a = 3, 2, b = 2, 1, and c = 7, 1. (b) Show, by means of a sketch, that there...
Problem 46E: Suppose that a and b are nonzero vectors that are not parallel and c is any vector in the plane...
Problem 47E: If r = x, y, z and r0 = x0, y0, z0, describe the set of all points (x, y, z) such that | r r0 | =...
Problem 48E: If r = x, y, r1 = x1, y1, and r2 = x2, y2, describe the set of all points (x, y) such that | r r1 |...
Problem 49E: Figure 16 gives a geometric demonstration of Property 2 of vectors. Use components to give an...
Problem 50E: Prove Property 5 of vectors algebraically for the case n =3. Then use similar triangles to give a...
Problem 51E: Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to...
Problem 52E
Problem 1DP
Problem 2DP
Problem 3DP
Problem 4DP
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