To find: The component form of the
Answer to Problem 5RE
The component form of the vector obtained by rotating the vector
Explanation of Solution
Given information:
The vector
Formula used:
Component form of a vector:
A two-dimensional vector
Polar coordinates of a vector:
A polar form of a vector
The formula of conversion from rectangular to polar coordinates is:
Here,
The vector
Calculation:
Let
Apply the formula of Magnitude of vectors to obtain the magnitude of the vector
Let the directional angle of the vector
Substitute
And,
Therefore, the vector
Now,
The vector
After rotation, the directional angle,
Apply the formula of Polar co-ordinates of vectors to obtain the vector
Substitute
And,
Simplify further to obtain:
and
Thus, the component form of the vector obtained by rotating the vector
Chapter 10 Solutions
CALCULUS-W/XL ACCESS
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