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A vector $a$ has components $2 p$ and 1 w.r.t a rectangluar cartesian system. It is rotated through a certain angle about the origin in the counter clockwise direction. With respect to the new system, if $a$ has components $p + 1, 1$ then $p =$

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$(1, \frac{- 1}{3})$

$(1, \frac{1}{3})$

$(- 1, \frac{1}{3})$

$(- 1, \frac{- 1}{3})$

answer is A.

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Detailed Solution

$4 p^{2} + 1 = {(p + 1)}^{2} + 1 \Rightarrow 2 p = p + 1, 2 p = - p - 1 p = 1 p = \frac{- 1}{3}$

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