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Question: If \(\mathbf{a} = 2\mathbf{i} + 2\mathbf{j} - \mathbf{k}\) and \(\mathbf{b} = 6\mathbf{i} - 3\mathbf...

If a=2i+2j−k\mathbf{a} = 2\mathbf{i} + 2\mathbf{j} - \mathbf{k} and b=6i−3j+2k,\mathbf{b} = 6\mathbf{i} - 3\mathbf{j} + 2\mathbf{k}, then the value of a×b\mathbf{a} \times \mathbf{b} is

A

2i+2j−k2\mathbf{i} + 2\mathbf{j} - \mathbf{k}

B

6i−3j+2k6\mathbf{i} - 3\mathbf{j} + 2\mathbf{k}

C

i−10j−18k\mathbf{i} - 10\mathbf{j} - 18\mathbf{k}

D

i+j+k\mathbf{i} + \mathbf{j} + \mathbf{k}

Answer

i−10j−18k\mathbf{i} - 10\mathbf{j} - 18\mathbf{k}

Explanation

Solution

\mathbf{i} & \mathbf{j} & \mathbf{k} \\ 2 & 2 & - 1 \\ 6 & - 3 & 2 \end{matrix} \right| = \mathbf{i} - 10\mathbf{j} - 18\mathbf{k}.$$