A) \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-\mathbf{k})=3\]
B) \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-\mathbf{k})=6\]
C) \[\mathbf{r}.(-\mathbf{i}-2\mathbf{j}+\mathbf{k})=3\]
D) None of these
Correct Answer: A
Solution :
The position vector of any point on the given line is \[\mathbf{i}+\mathbf{j}+\lambda (2\mathbf{i}+\mathbf{j}+4\mathbf{k})\]or \[(2\lambda +1)\mathbf{i}+(\lambda +1)\mathbf{j}+4\lambda \mathbf{k}\] which lies on \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-\mathbf{k})=3\]. Hence, the plane \[\mathbf{r}.(\mathbf{i}+2\mathbf{j}-\mathbf{k})=3\] contains the given line.
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