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Math
Calculus
CALCULUS: EARLY TRANSCENDENTALS
Chapter 12.4, Problem 45E
Chapter 12.4, Problem 45E
BUY
CALCULUS: EARLY TRANSCENDENTALS
9th Edition
ISBN:
9780357375808
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: Find the cross product a b and verify that it is orthogonal to both a and b. 1. a = 2, 3, 0, b = 1,...
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E: Find the cross product a b and verify that it is orthogonal to both a and b. 6. a = ti + cos tj +...
Problem 7E
Problem 8E: If a = i 2k and b = j + k, find a b. Sketch a, b, and a b has vectors starting at the origin.
Problem 9E: Find the vector, not with determinants, but by using properties of cross products. 9. (i j) k
Problem 10E: Find the vector, not with determinants, but by using properties of cross products. 10. k (i 2j)
Problem 11E: Find the vector, not with determinants, but by using properties of cross products. 11. (j k) (k ...
Problem 12E: Find the vector, not with determinants, but by using properties of cross products. 12. (i + j) (i ...
Problem 13E: State whether each expression is meaningful. If not, explain why. If so, state whether it is a...
Problem 14E: Find uv and determine whether uv is directed into the page or out of the page. 14.
Problem 15E: Find uv and determine whether uv is directed into the page or out of the page. 15.
Problem 16E
Problem 17E: If a = 2, 1, 3 and b = 4, 2, 1, find a b and b a.
Problem 18E
Problem 19E: Find two unit vectors orthogonal to both 3, 2, 1 and 1, 1, 0.
Problem 20E: Find two unit vectors orthogonal to both j k and i + j.
Problem 21E: Show that 0 a = 0 = a 0 for any vector a in V3.
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E: Find the area of the parallelogram with vertices A(3, 0), B(1, 3). C(5, 2), and D(3. 1).
Problem 28E: Find the area of the parallelogram with vertices P(1, 0, 2), Q(3, 3, 3). R(7, 5, 8), and S(5,2, 7).
Problem 29E: (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R , and (b) find the...
Problem 30E: (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R , and (b) find the...
Problem 31E: (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R , and (b) find the...
Problem 32E: (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and (b) find the...
Problem 33E: Find the volume of the parallelepiped determined by the vectors a, b. and c. 33. a = 1, 2, 3), b =...
Problem 34E: Find the volume of the parallelepiped determined by the vectors a, b. and c. 34. a = i + j , b = j +...
Problem 35E: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. 35. P(2, 1, 0), Q(2. 3....
Problem 36E: Find the volume of the parallelepiped with adjacent edges PQ, PR. and PS. 36. P(3, 0, 1), Q(1, 2,...
Problem 37E: Use the scalar triple product to verify that the vectors u = i + 5j 2k, v = 3i j, and w = 5i + 9j ...
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E: Let v = 5j and let u be a vector with length 3 that starts at the origin and rotates in the...
Problem 43E: If a b = 3 and a b = 1, 2, 2, find the angle between a and b.
Problem 44E: (a) Find all vectors v such that 1, 2, 1 x v = 3, 1, 5) (b) Explain why there is no vector v such...
Problem 45E
Problem 46E
Problem 47E: Show that | a b |2 = | a |2| b |2 (a b)2
Problem 48E
Problem 49E: Prove that (a b) (a + b) = 2(a b).
Problem 50E: Prove Properly 6 of cross products, that is, a (b c) = (a c)b (a b)c
Problem 51E: Use Exercise 50 to prove that a (b c) + b (c a) + c (a b) = 0
Problem 52E: Prove that (ab)(cd)=|acbcadbd|
Problem 53E: Suppose that a 0. (a) If a b = a c, does it follow that b = c? (b) If a b = a c, does it follow...
Problem 54E: If v1, v2, and v3 are noncoplanar vectors, let k1=v2v3v1(v2v3) k2=v3v1v1(v2v3) k3=v1v2v1(v2v3)...
Problem 1DP
Problem 2DP
Problem 3DP
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