In \( R^{2} \), if the magnitude of the projection vector of \( \ma...

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In \( R^{2} \), if the magnitude of the projection vector of
\( \mathrm{P} \) the vector \( \alpha \hat{i}+\beta \hat{j} \) on \( \sqrt{3} \hat{i}+\hat{j} \) is \( \sqrt{3} \) and if

W \( \alpha=2+\sqrt{3} \beta \), then possible value(s) of \( |\alpha| \), is (are)
(1) 1, 2
(2) 3,4
(3) 4,5
(4) 3
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