Question

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

• A. $9:1$
• B. $1:9$
• C. $-1:9$
• D. $-9:1$

Answer 1

Answer: (D)

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 $=-9:1$