Explanation Given: Let v lies in the y z -plane. Formula used: The dot product of the two vectors is a scalar. Formula for the Dot Product of the vectors: 〈 a , b , c 〉 ⋅ 〈 d , e , f 〉 = a d + b e + c f Calculation: Let v lies in the y z -plane. Consider the vector v = 〈 0 , y , z 〉 . Part a: We have to find the dot product of v ⋅ 〈 0 , 2 , 1 〉 . v ⋅ 〈 0 , 2 , 1 〉 = 〈 0 , y , z 〉 ⋅ 〈 0 , 2 , 1 〉 = 0 ( 0 ) + y ( 2 ) + z ( 1 ) = 0 + 2 y + z = 2 y + z Hence, the dot product cannot be zero for all choices of v = 〈 0 , y , z 〉 . Part b: We have to find the dot product of v ⋅ k . Let the value of k is 〈 0 , 0 , 1 〉 . v ⋅ k = 〈 0 , y , z 〉 ⋅ 〈 0 , 0 , 1 〉 = 0 ( 0 ) + y ( 0 ) + z ( 1 ) = 0 + 0 + z = z Hence, the dot product cannot be zero for all choices of v = 〈 0 , y , z 〉 ...

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 12.3, Problem 36E

To determine

Which of the following dot products is equal to zero for all choices of $v$ ?

a. $v \cdot 〈 0, 2, 1 〉$

b. $v \cdot k$

c. $v \cdot 〈 - 3, 0, 0 〉$

d. $v \cdot j$

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Chapter 12.3, Problem 35E

Chapter 12.3, Problem 37E

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Chapter 12 Solutions

Calculus: Early Transcendentals

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E

Knowledge Booster

Which of the following dot products is equal to zero for all choices of v ? a. v ⋅ 〈 0 , 2 , 1 〉 b. v ⋅ k c. v ⋅ 〈 − 3 , 0 , 0 〉 d. v ⋅ j

Which of the following dot products is equal to zero for all choices of v? a. v⋅〈0,2,1〉 b. v⋅k c. v⋅〈−3,0,0〉 d. v⋅j

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Chapter 12 Solutions

Which of the following dot products is equal to zero for all choices of $v$ ?

a. $v \cdot 〈 0, 2, 1 〉$

b. $v \cdot k$

c. $v \cdot 〈 - 3, 0, 0 〉$

d. $v \cdot j$