$A$ vector $\vec{a}$ has components $3p$ 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,$\vec{a}$ has components $p+1$ and $\sqrt{10}$,then a value of $p$ is equal to
- A$1$
- B$-\frac{5}{4}$
- C$\frac{4}{5}$
- D$-1$
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