Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Textbook Question
Chapter 12.3, Problem 1PT
For a = 2i + 3j − 4k and b = −i + 2j − k, a · b =
- a) 0
- b) 8
- c) 10
- d) 12
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u, v and w are three coplanar vectors:
⚫ w has a magnitude of 10 and points along the positive x-axis
⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x-
axis
⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x-
axis
⚫ vector v is located in between u and w
a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane.
b) If possible, find
w × (ū+v)
Support your answer mathematically or a with a written explanation.
c) If possible, find
v. (ū⋅w)
Support your answer mathematically or a with a written explanation.
d) If possible, find
u. (vxw)
Support your answer mathematically or a with a written explanation.
Note: in this question you can work with the vectors in geometric form or convert
them to algebraic vectors.
Question 3 (6 points)
u, v and w are three coplanar vectors:
⚫ w has a magnitude of 10 and points along the positive x-axis
⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x-
axis
⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x-
axis
⚫ vector v is located in between u and w
a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane.
b) If possible, find
w × (u + v)
Support your answer mathematically or a with a written explanation.
c) If possible, find
v. (ū⋅ w)
Support your answer mathematically or a with a written explanation.
d) If possible, find
u (v × w)
Support your answer mathematically or a with a written explanation.
Note: in this question you can work with the vectors in geometric form or convert
them to algebraic vectors.
Chapter 12 Solutions
Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 12.1 - Prob. 1PTCh. 12.1 - Prob. 2PTCh. 12.1 - Prob. 3PTCh. 12.1 - Prob. 4PTCh. 12.1 - Prob. 5PTCh. 12.2 - Prob. 1PTCh. 12.2 - Prob. 2PTCh. 12.2 - Prob. 3PTCh. 12.2 - Prob. 4PTCh. 12.2 - Prob. 5PT
Ch. 12.2 - Prob. 6PTCh. 12.3 - For a = 2i + 3j 4k and b = i + 2j k, a b = a) 0...Ch. 12.3 - Prob. 2PTCh. 12.3 - Prob. 3PTCh. 12.3 - Prob. 4PTCh. 12.3 - Prob. 5PTCh. 12.3 - Prob. 6PTCh. 12.4 - Prob. 1PTCh. 12.4 - Prob. 2PTCh. 12.4 - Prob. 3PTCh. 12.4 - Prob. 4PTCh. 12.4 - Prob. 5PTCh. 12.4 - Prob. 6PTCh. 12.5 - The equation of the line through (4, 10, 8) and...Ch. 12.5 - True or False: These lines are skew:...Ch. 12.5 - The equation of the plane through 7, 2, 3 with...Ch. 12.5 - The equation of the plane formed by the two lines...Ch. 12.5 - The distance from (1, 2, 1) to the plane 6x + 5y +...Ch. 12.5 - A normal vector to the plane 2x + 3y + 6z =20 is:...Ch. 12.6 - Prob. 1PTCh. 12.6 - Prob. 2PTCh. 12.6 - Prob. 3PTCh. 12.6 - The graph at the right has equation: a)...Ch. 12.6 - Prob. 5PTCh. 12.6 - Prob. 6PT
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