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Question

A vector a has components 2p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system. a has components p + 1 and 1, 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 B p=1 or p=13
Here, a=(2p)^i+^j,
When the system is rotated, the new components of a are (p + 1) and 1.
i.e. b=(p+1)^i+^j
But |a|2=|b|2
4p2+1=(p+1)2+14p2=p2+2p+13p22p1=0(3p+1)(p1)=0p=1,1/3

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