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Question

A vector a has components 2p and 1 with respect to a rectangular Cartesian system. The system is rotated through a certain angle about the origin in the counterclockwise sense. If a has components p+1 and 1 with respect to the new system, then

A
p=0
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B
p=1 or p=13
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C
p=1 or p=13
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D
p=1 or p=1
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Solution

The correct option is D p=1 or p=13
Here a=(2p)^i+^j when a system is rotated the new component of a are p+1 and 1
b=(p+1)^i+^j
|a|2=b2
4p2+1=(p+1)2+1
4p2=p2+2p+1
3p22p1=0
(3p+1)(p1)=0
3p+1=0,p1=0
p=13,1


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