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A vector a has components \( 3 p \) 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 new system, a has components \( p+1 \) and \( \sqrt{10} \), then a value of \( p \) is equal to:
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The correct answer is:
\( -1 \)
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