Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
Chapter 10, Problem 21RE
(a)
To determine
To find: The component form of the
(a)
Expert Solution
Answer to Problem 21RE
The component form of the vector v with initial point (4,−2,1) and terminal point (−1,5,0) is 〈−5,7,−1〉 .
Explanation of Solution
Given information:
The vector v has initial point (4,−2,1) and terminal point (−1,5,0) .
Formula Used:
The component form of a vector v with initial point P(p1,p2,p3) and terminal point Q(q1,q2,q3) is v=〈q1−p1,q2−p2,q3−p3〉 .
Calculation:
Substitute 4 , −2 , 1 for p1 , p2 , p3 and −1 , 5 , 0 for q1 , q2 , q3 in the formula.
v=〈q1−p1,q2−p2,q3−p3〉=〈−1−4,5−(−2),0−1〉=〈−5,7,−1〉
Therefore, the component form of the vector v with initial point (4,−2,1) and terminal point (−1,5,0) is 〈−5,7,−1〉 .
(b)
To determine
To find: The magnitude of vector v with initial point (4,−2,1) and terminal point (−1,5,0) .
(b)
Expert Solution
Answer to Problem 21RE
The magnitude of vector v with initial point (4,−2,1) and terminal point (−1,5,0) is 5√3 .
Explanation of Solution
Given information:
The vector v has initial point (4,−2,1) and terminal point (−1,5,0) .
Formula used:
The magnitude of any vector v with component form v=〈v1,v2,v3〉 is
Calculation:
As calculated in part (a), the component form of the vector
Substitute
Therefore, the magnitude of vector
(c)
To determine
To find: A unit vector in the direction of
(c)
Expert Solution
Answer to Problem 21RE
The unit vector in the direction of
Explanation of Solution
Given information:
The vector
Formula used:
The unit vector in the direction of vector
Calculation:
As calculated in part (a), the component form of the vector
As calculated in part (b), the magnitude of the vector
Substitute
Therefore, the unit vector in the direction of
Chapter 10 Solutions
Precalculus with Limits: A Graphing Approach
Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
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