a vector is rotated through angle theta.what is the magnitude of change in vector?
a) 2a cos (theta/2)
b) 2a sin (theta/2)
c) 2a cos theta
d) 2a sin theta
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Answer:b
Explanation:
Let a1 and a2 denotes the initial and final vectors and c denotes change in vector
C=a2-a1
|c|=√(a1suare+a2square-2a1a2costheta)
One rotation the magnitude of vectors does not change only its direction changes
|c|=√(a^2+a^2-2a^2costheta)
=√(2a^2-2a^2costheta)
√2a^2(1-costheta)
= √2a^2(2sin^2theta/2)
=2a sin theta/2
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