A) \[5(-\,i+3j+4k)\]
B) \[4(-\,i+3j+4k)\]
C) \[5(-\,i-3j-4k)\]
D) \[4(i+3j+4k)\]
Correct Answer: A
Solution :
\[\vec{A}\times \vec{B}=\left| \,\begin{matrix} \mathbf{i} & \mathbf{j} & \,\,\mathbf{k} \\ 1 & -2\,\, & -3 \\ 2 & 1 & -1\, \\ \end{matrix}\, \right|=\mathbf{i}(2+3)-\mathbf{j}(-1+6)+\mathbf{k}(1+4)\] \[=5\mathbf{i}-5\mathbf{j}+5\mathbf{k}\] Now \[(\vec{A}\times \vec{B})\times \vec{C}=\left| \,\begin{matrix} \mathbf{i} & \mathbf{j} & \,\mathbf{k} \\ 5\, & -5\,\, & \,\,5 \\ 1 & 3 & -2 \\ \end{matrix}\, \right|\] \[=\mathbf{i}(10-15)-\mathbf{j}(-10-5)+\mathbf{k}(15+5)\] \[=-5\mathbf{i}+15\mathbf{j}+20\mathbf{k}\]\[=5(-\mathbf{i}+3\mathbf{j}+4\mathbf{k})\].
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