A) \[4\mathbf{i}+3\mathbf{j}+5\mathbf{k}\]
B) \[4\mathbf{i}-3\mathbf{j}+7\mathbf{k}\]
C) \[4\mathbf{i}+3\mathbf{j}+7\mathbf{k}\]
D) \[4\mathbf{i}+3\mathbf{j}-7\mathbf{k}\]
Correct Answer: C
Solution :
\[\overrightarrow{OA}=2\mathbf{i}+3\mathbf{j}-\mathbf{k},\] \[\overrightarrow{OP}=3(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[\overrightarrow{OB}=?\] we have \[\overrightarrow{OP}=\frac{\overrightarrow{OA}+\overrightarrow{OB}}{2}\] \[\Rightarrow \overrightarrow{OB}=2\overrightarrow{OP}-\overrightarrow{OA}\] \[=4\mathbf{i}+3\mathbf{j}+7\mathbf{k}\] Trick : By inspection, middle point of \[4\mathbf{i}+3\mathbf{j}+7\mathbf{k}\] and \[2\mathbf{i}+3\mathbf{j}-\mathbf{k}\] is \[3\,(\mathbf{i}+\mathbf{j}+\mathbf{k}).\]You need to login to perform this action.
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