A) (2, ? 3)
B) (? 2, 3)
C) (2, 3)
D) (? 2, ? 3)
Correct Answer: A
Solution :
If A, B, C are collinear. Then \[\overrightarrow{AB}=\lambda \,\overrightarrow{BC}\] Þ \[2\mathbf{i}+(4-x)\mathbf{j}+4\mathbf{k}=\lambda \,[(y-3)\mathbf{i}-6\mathbf{j}-12\mathbf{k}]\] \[\Rightarrow \,\,\,2=(y-3)\lambda \] .....(i) and \[4-x=-6\,\lambda \] .....(ii) Þ \[4=-12\,\lambda \,\,\,\,\,\Rightarrow \,\,\lambda =\frac{-1}{3}\] By (i), \[y=-3\] and by (ii), \[x=2\]; \[\therefore \,\,\,(x,\,y)=(2,\,-3).\]You need to login to perform this action.
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