question_answer

Let A be the point (1, 2, 3) and B be a point on the line\[\overset{\to }{\mathop{r}}\,=(\hat{i}-\hat{j}+5\hat{k})+\lambda (-2\hat{i}+3\hat{j}+4\hat{k})\] Then the value of '\[\lambda \]' for which line AB is perpendicular to the plane \[4x+9y-18z=1\] is

A) \[\frac{-2}{3}\]                                 

B) \[\frac{-1}{6}\]

C) \[\frac{2}{5}\]                                   

D) \[\frac{1}{3}\]

Correct Answer: C

Solution :

Any point on the line \[B(1-2\lambda ,-1+3\lambda ,5+4\lambda )\] \[\therefore \]Direction ratios AB are \[(-2\lambda ,3\lambda -3,4\lambda +2)\] AB is parallel the normal of the plane \[\frac{-2\lambda }{4}=\frac{3\lambda -3}{9}=\frac{4\lambda +2}{-18}\Rightarrow \lambda =\frac{2}{5}\]Ans.