A vector has components 2p and 1 eith respect to a rectangular cartesian system. This system is rota

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

Accepted Answer

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

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