A) \[\mathbf{i}+5\mathbf{j}-4\mathbf{k}\]
B) \[\mathbf{i}-5\mathbf{j}+4\mathbf{k}\]
C) \[-\frac{1}{2}\,(\mathbf{i}+5\mathbf{j}-4\mathbf{k})\]
D) None of these
Correct Answer: C
Solution :
\[\mathbf{r}=\mathbf{p}+\lambda \,\mathbf{q}\Rightarrow \mathbf{r}\,.\,\mathbf{q}=\mathbf{p}\,.\,\mathbf{q}+\lambda \,\mathbf{q}\,.\,\mathbf{q}\] \[\Rightarrow 0=7+14\lambda \,\,\Rightarrow \lambda \,\,=-\frac{1}{2}\] Therefore, \[\mathbf{r}=-\frac{1}{2}(\mathbf{i}+5\mathbf{j}-4\mathbf{k}).\]
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