A) \[5\mathbf{i}+5\mathbf{j}-15\mathbf{k}\]
B) \[0\]
C) \[12\mathbf{j}+4\mathbf{k}\]
D) \[-3\mathbf{i}+6\mathbf{j}-3\mathbf{k}\]
Correct Answer: A
Solution :
\[\mathbf{a}=-\mathbf{i}+2\mathbf{j}-\mathbf{k},\,\,\mathbf{b}=\mathbf{i}+\mathbf{j}-3\mathbf{k},\,\,\mathbf{c}=-4\mathbf{i}-\mathbf{k}\] \[\therefore \] \[\mathbf{a}\times (\mathbf{b}\times \mathbf{c})+(\mathbf{a}\cdot \mathbf{b})\mathbf{c}=(\mathbf{a}\cdot \mathbf{c})\mathbf{b}\] \[=(4+1)(\mathbf{i}+\mathbf{j}-3\mathbf{k})\] \[=5\mathbf{i}+5\mathbf{j}-15\mathbf{k}\]
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