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Question: If \(\mathbf{a} = 2\mathbf{i} + \mathbf{j} - \mathbf{k},\mathbf{b} = \mathbf{i} + 2\mathbf{j} + \mat...

If a=2i+j−k,b=i+2j+k\mathbf{a} = 2\mathbf{i} + \mathbf{j} - \mathbf{k},\mathbf{b} = \mathbf{i} + 2\mathbf{j} + \mathbf{k} and c=i−j+2k,\mathbf{c} = \mathbf{i} - \mathbf{j} + 2\mathbf{k}, then

a.(b×c)=\mathbf{a}.(\mathbf{b} \times \mathbf{c}) =

A

6

B

10

C

12

D

24

Answer

12

Explanation

Solution

\mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 2 & 1 \\ 1 & - 1 & 2 \end{matrix} \right| = \mathbf{a}.(5\mathbf{i} - \mathbf{j} - 3\mathbf{k})$$ $= (2\mathbf{i} + \mathbf{j} - \mathbf{k}).(5\mathbf{i} - \mathbf{j} - 3\mathbf{k}) = 10 - 1 + 3 = 12$.