Concept explainers
Writing
(a)
To calculate: Acomponent form of u and v where
Answer to Problem 1RE
Solution:
Component form of uand v is
Explanation of Solution
Given:
Formula used:
If
Calculation:
If u
and
The component form of u is
If v
and
The component form of v is
(b)
To calculate: u and vas the linear combination of the standard unit vectors i and jwhere
Answer to Problem 1RE
Solution:
The vectors
Explanation of Solution
Given:
Formula used:
If
Calculation:
According to the calculation of part (a), a component form of u and vis
Therefore, the vectors
(c)
To calculate: Magnitudes of u and vwhere
Answer to Problem 1RE
Solution:
The magnitude of u is
Explanation of Solution
Given:
Formula used:
According to the Distance Formula, the length (or magnitude) of vectoru is:
Calculation:
As per part (a),
and v=
Therefore, the magnitude of u is
(d)
To calculate: The value of
Answer to Problem 1RE
Solution:
The value of
Explanation of Solution
Given:
Formula used:
The scalar multiple of c and u is the vector:
The vector sum of u and v is the vector:
Calculation:
According to the calculation of part (a), a component form of u and v is
Find the value of
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Chapter 11 Solutions
CALCULUS: EARLY TRANSCENDENTAL FUNCTIO
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