VectorHard
Question
A vector 
has components 2p and 1 eith 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. has components p + 1 and 1, then
has components 2p and 1 eith 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. has components p + 1 and 1, thenOptions
A.p = 0
B.p = 1 or p = - 
C.p = - 1 or p =
D.p = 1 or p = -1
Solution
Here, 
when a system is rotated, the new component of 
are (p + 1) and 1.
ie,
⇒
or 4p2 + 1 = (p + 1)2 + 1
⇒ 4p2 = p2 + 2p + 1
⇒ 3p2 - 2p - 1 = 0
⇒ (3p + 1)(p - 1) = 0
⇒ p = 1,- 1/ 3
when a system is rotated, the new component of are (p + 1) and 1. ie,
⇒
or 4p2 + 1 = (p + 1)2 + 1
⇒ 4p2 = p2 + 2p + 1
⇒ 3p2 - 2p - 1 = 0
⇒ (3p + 1)(p - 1) = 0
⇒ p = 1,- 1/ 3
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