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Question: If \(\mathbf{a} = 3\mathbf{i} - 2\mathbf{j} + 2\mathbf{k},\mathbf{b} = 6\mathbf{i} + 4\mathbf{j} - 2...

If a=3i−2j+2k,b=6i+4j−2k\mathbf{a} = 3\mathbf{i} - 2\mathbf{j} + 2\mathbf{k},\mathbf{b} = 6\mathbf{i} + 4\mathbf{j} - 2\mathbf{k} and c=3i−2j−4k\mathbf{c} = 3\mathbf{i} - 2\mathbf{j} - 4\mathbf{k},

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

A

122

B

– 144

C

120

D

– 120

Answer

– 144

Explanation

Solution

3 & - 2 & 2 \\ 6 & 4 & - 2 \\ 3 & - 2 & - 4 \end{matrix} \right|$$ $$= 3\lbrack - 16 - 4\rbrack + 2\lbrack - 24 + 6\rbrack + 2\lbrack - 12 - 12\rbrack$$ = – 60 – 36 – 48 = – 144.