Please solve this. I have to cross check my answer.

D e a r s t u d e n t, \vec{p} = k (\vec{a} \times \vec{b}) \vec{a} \times \vec{b} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 4 & 2 \\ 3 & - 2 & 7 \end{matrix}| = \hat{i} (28 + 4) - \hat{j} (7 - 6) + \hat{k} (- 2 - 12) = 32 \hat{i} - \hat{j} - 14 \hat{k} \vec{p} = k (32 \hat{i} - \hat{j} - 14 \hat{k}) \vec{p} . \vec{c} = k (32 \hat{i} - \hat{j} - 14 \hat{k}) . (2 \hat{i} - \hat{j} + 4 \hat{k}) 18 = k (32 \times 2 - 1 \times (- 1) - 14 \times 4) 18 = k (64 + 1 - 56) 18 = 2 k k = 2 \vec{p} = 2 (32 \hat{i} - \hat{j} - 14 \hat{k}) R e g a r d s

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