$A$ vector $\vec{a}$ has components $2p$ and $1$ with respect to a two-dimensional rectangular Cartesian system. This system is rotated through a certain angle $\theta$ about the origin in the counter-clockwise direction. If $\vec{a}$ has components $p+1$ and $1$ with respect to the new system,then:
- A$p=1$ or $p=\frac{-1}{3}$
- B$p=-1$ or $p=\frac{1}{3}$
- C$p=1$ or $p=-1$
- D$p=0$ or $p=\frac{1}{2}$
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