JEE Advance - Mathematics (1986 - No. 16)
A vector $$\overline a $$ 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, $$\overline a $$ has components $$p + 1$$ and $$1$$, then
$$p = 0$$
$$p = 1$$ or $$p = - {1 \over 3}$$
$$\,p = - 1$$ or $$p = {1 \over 3}$$
$$p = 1$$ or $$p = -1$$