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If in the shown figure \( \overrightarrow{\mathrm{AC}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}} \) and \( \overrightarrow{\mathrm{BD}}=\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+\hat{\mathrm{k}} \) then \( \overrightarrow{\mathrm{BC}} \) is
(A) \( \frac{3}{2} \hat{\mathrm{i}}-\frac{1}{2} \hat{\mathrm{j}}+5 \hat{\mathrm{k}} \)
(B) \( \frac{3}{2} \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}} \)
(C) \( 2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+5 \hat{\mathrm{k}} \)
(D) \( \hat{i}-\frac{1}{2} \hat{j}+\frac{5}{2} \hat{k} \)
\( \mathrm{P} \)
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