Q.7 If \(\bar{a} = 3\hat{i} - \hat{j} + 2\hat{k},\ \bar{b} = 2\hat{i} + \hat{j} - \hat{k}\), then find \(|\bar{a} \times \bar{b}|\)
Best answer
Answer: \(|\bar{a} \times \bar{b}| = 5\sqrt{3}\)
\(\bar{a} \times \bar{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & -1 & 2 \\ 2 & 1 & -1 \end{vmatrix} = \hat{i}(1 - 2) - \hat{j}(-3 - 4) + \hat{k}(3 + 2) = -\hat{i} + 7\hat{j} + 5\hat{k}\)
\(|\bar{a} \times \bar{b}| = \sqrt{1 + 49 + 25} = \sqrt{75} = 5\sqrt{3}\).
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