A) \[15+\sqrt{157}\]
B) \[15-\sqrt{157}\]
C) \[\sqrt{15}-\sqrt{157}\]
D) \[\sqrt{15}+\sqrt{157}\]
Correct Answer: A
Solution :
\[\mathbf{a}=4\mathbf{i}+2\mathbf{j}-4\mathbf{k}\Rightarrow \,\,|\mathbf{a}|\,\,=\sqrt{16+16+4}=6\] \[\mathbf{b}=-3\mathbf{i}+2\mathbf{j}+12\mathbf{k}\Rightarrow \,\,|\mathbf{b}|\,\,=\,\,\sqrt{144+4+9}=\sqrt{157}\] \[\mathbf{c}=-\mathbf{i}-4\mathbf{j}-8\mathbf{k}\Rightarrow \,\,|\mathbf{c}|\,\,=\,\,\sqrt{64+16+1}=9\] Hence perimeter is \[15+\sqrt{157}.\]You need to login to perform this action.
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