If \( \vec{a} \) of magnitude 50 is collinear with the vector P \( ...

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If \( \vec{a} \) of magnitude 50 is collinear with the vector
P \( \overrightarrow{\mathrm{b}}=6 \hat{i}-8 \hat{\mathrm{j}}-\frac{15 \hat{\mathrm{k}}}{2} \), and makes an acute angle with the

W positive direction of \( z \)-axis, then the vector \( \vec{a} \) is equal to
(1) \( 24 \hat{\mathrm{i}}-32 \hat{\mathrm{j}}+30 \hat{\mathrm{k}} \)
(2) \( -24 \hat{\mathrm{i}}+32 \hat{\mathrm{j}}+30 \hat{\mathrm{k}} \)
(3) \( 16 \hat{i}-16 \hat{j}-15 \hat{\mathrm{k}} \)
(4) \( -12 \hat{i}+16 \hat{j}-30 \hat{k} \)
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