Velocity of a particle of mass \( 2 \mathrm{~kg} \) changes from \( \vec{v}_{1}=(-2 \hat{i}-2 \h...

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Velocity of a particle of mass \( 2 \mathrm{~kg} \) changes from \( \vec{v}_{1}=(-2 \hat{i}-2 \hat{j}) \mathrm{m} / \mathrm{s} \) to \( \vec{v}_{2}=(\hat{i}-\hat{j}) \mathrm{m} / \mathrm{s} \) after colliding with a plane surface.
(1) The angle made by the plane surface with the positive \( x \)-axis is \( 90^{\circ}+\tan ^{-1}\left(\frac{1}{3}\right) \).
(2) The angle made by the plane surface with the positive \( x \)-axis is \( \tan ^{-1}\left(\frac{1}{3}\right) \).
(3) The direction of change in momentum makes an angle \( \tan ^{-1}\left(\frac{1}{3}\right) \) with the positive \( x \)-axis.
(4) The direction of change in momentum makes an angle \( 90^{\circ}+\tan ^{-1}\left(\frac{1}{3}\right) \) with the plane surface.
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