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If \( \vec{A}=2 \hat{i}+\sqrt{7} \hat{\mathrm{j}} \) and \( \vec{B}=5 \hat{i}+\sqrt{7} \hat{\mathrm{j}}-3 \hat{\mathrm{k}} \), then the
\( \mathrm{P} \) vector whose magnitude is equal to \( \overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}} \) and

W parallel to \( \vec{B}-\vec{A} \) is :
(1) \( \frac{17}{\sqrt{2}}(\hat{\mathrm{k}}-\hat{\mathrm{j}}) \)
(2) \( \frac{17}{\sqrt{2}}(\hat{i}-\hat{k}) \)
(3) \( 3 \hat{\mathrm{i}}-3 \hat{\mathrm{k}} \)
(4) \( 3 \hat{k}-3 \hat{i} \)
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