A) i + j ? k
B) i ? j + k
C) 3i + j ? k
D) 3i ? j + k
Correct Answer: C
Solution :
Let \[\mathbf{r}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}\], then \[\mathbf{r}\times \mathbf{a}=\mathbf{b}\times \mathbf{a}\] Þ \[(\mathbf{r}-\mathbf{b})\times \mathbf{a}=0\] \[\Rightarrow \left| \begin{align} & \,\,\,\,i\,\,\,\,\,\,\,\,\,\,j\,\,\,\,\,\,\,\,k \\ & x-2\,\,\,\,\,\,y\,\,\,\,\,\,z+1 \\ & \,\,\,\,1\,\,\,\,\,\,\,\,\,1\,\,\,\,\,\,\,\,\,\,0 \\ \end{align} \right|=0\], \[\therefore z=-1,\,\,x-y=2\] Now \[\mathbf{r}\times \mathbf{b}=\mathbf{a}\times \mathbf{b}\] Þ \[(\mathbf{r}-\mathbf{a})\times \mathbf{b}=0\] \[\therefore y=1,\,\,x+2z=1\] \[\Rightarrow x=3,\,\,y=1,\,\,z=-1\] \\[\mathbf{r}=3\mathbf{i}+\mathbf{j}-\mathbf{k}\].
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