Representation of Vectors

Q. 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 anti-clockwise sense. If $a$ has components $p+1$ and $1$ with respect to the new system, then

1. $p=0$
2. $p=1$ or $-\frac{1}{3}$
3. $p=-1$ or $\frac{1}{3}$
4. $p=1$ or $-1$

Q.

A vector $\overrightarrow{a}$ 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, $\overrightarrow{a}$ has components (p+1) and 1, then

1. $p=0$

2. $p=1orp=-\frac{1}{3}$

3. $p=1orp=-1$

4. $p=-1orp=\frac{1}{3}$