Three forces \( \vec{P}, \vec{O} \) and \( \vec{R} \) each of 15 units, act along \( A B, B C \) and \( C A \) respectively. The position
\( \mathrm{P} \) vectors of \( A, B \) and \( C \) are \( \overrightarrow{O A}=2 \vec{i}-j+3 \vec{k}, \overrightarrow{O B}=5 \vec{i}+3 j-2 \vec{k} \) and \( \overrightarrow{O C}=2 \vec{i}+2 j+3 \vec{k} \). The
W resultant force vector is
(a) \( \left(12 \frac{9}{\sqrt{2}}-7 \sqrt{3}\right) \vec{i}-(9-6 \sqrt{2}+\sqrt{3}) \vec{j}+\left(5 \sqrt{3}-\frac{15}{\sqrt{2}}\right) \vec{k} \)
(b) \( \left(12+\frac{9}{\sqrt{2}}-7 \sqrt{3}\right) \vec{i}+(9-6 \sqrt{2}+\sqrt{3}) \vec{j}+\left(\frac{15}{\sqrt{2}}-5 \sqrt{3}\right) \vec{k} \)
(c) \( 75 \vec{i}+60 \vec{j}+60 \vec{k} \)
(d) none of these
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