Q.

A vector of magnitude b is rotated through angle θ . What is the magnitude of the change in the vector

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a

2bsinθ2

b

2bcosθ2

c

2b

d

2bcosθ

answer is A.

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Detailed Solution

PQ→+QR→=PR→∴QR→=b'→-b→ Now |b'→−b→|2=(b'→−b→).(b'→-b→)                        =b'2-2bb'cosθ+b2                        =2b2(1−cosθ)              [∵b'=b]b'→−b→=2b1−cosθ          =2b(2sinθ2)          =2bsinθ2
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A vector of magnitude b is rotated through angle θ . What is the magnitude of the change in the vector