Q. If the position vectors of two points P and Q are respectively $ 9\,\hat{i}-\hat{j}+5\hat{k} $ and $ \hat{i}+3\hat{j}+5\hat{k} $ and the line segment PQ intersects the YOZ plane at a point R, then $ PR:RQ $ is equal to
J & K CETJ & K CET 2005
Solution:
Position vector of $ P=9\hat{i}-\hat{j}+5\hat{k}=(9,-1,5) $
and position vector of Q
$ =\hat{i}+3\hat{j}+5\hat{k}=(1,3,5) $
Let $ PR:RQ=m:1 $
$ \because $ PQ intersects the YOZ plane.
$ \therefore $ x-coordinate of
$ R=0 $ $ \Rightarrow $
$ \frac{9\times 1+m\times 1}{m+1}=0 $
$ \Rightarrow $ $ 9+m=0 $
$ \Rightarrow $ $ m=-9 $
$ \therefore $ Ratio $ =-9:1 $
