(a)
The vector
(a)
Answer to Problem 2T
The vector
Explanation of Solution
Given:
The two vectors are
Formula used: The scalar multiplication of a vector
The subtraction of the vectors
Calculation:
Substitute
Thus, the vector
(b)
The value of
(b)
Answer to Problem 2T
The value of
Explanation of Solution
Given:
The two vectors are
Formula used: The addition of the vectors
The magnitude of a vector
Calculation:
Substitute 1 for
The vector
Substitute
Thus, the value of
(c)
The value of
(c)
Answer to Problem 2T
The value of
Explanation of Solution
Given:
The two vectors are
Formula used: The Dot Product of the vectors
Calculation:
Substitute 1 for
Thus, the value of
(d)
Whether the vectors
(d)
Answer to Problem 2T
The vectors
Explanation of Solution
The two vectors are perpendicular if and only if the dot product
of the vectors is 0, i.e., the vectors u and v are perpendicular if
From part (c), the value of
Thus, the vectors
Chapter 9 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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