A) \[(0,\text{ }6,-1)\]and\[(1,-2,-1)\]
B) \[(0,\text{ }6,-1)\]and\[(-1,-4,-2)\]
C) \[(1,-2,-1)\]and \[(1,4,-2)\]
D) \[(1,-2,-1)\]and \[(0,-6,1)\]
E) \[(1,4,-2)\]and\[(2,10,-3)\]
Correct Answer: C
Solution :
Equation of line passing through\[\overrightarrow{a}\]and\[\overrightarrow{b}\]is \[\overrightarrow{a}+\lambda (\overrightarrow{b}-\overrightarrow{a})\] \[\Rightarrow \] \[\overrightarrow{b}-\overrightarrow{a}=6\overrightarrow{j}-\vec{k}\] \[\Rightarrow \] \[\overrightarrow{b}=6\overrightarrow{j}-\overrightarrow{k}+\hat{i}-2\hat{j}-\hat{k}\] \[=\hat{i}+4\hat{j}-2\hat{k}\] \[\therefore \]Given line passes through\[(1,-2,-1)\]and\[(1,4,-2)\].
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