Question

If $P=(3,4,5)$, $Q=(4,6,3)$, $R=(-1,2,4)$ and $S=(1,0,5)$ are four points, then the projection of $RS$ on $PQ$ is

• A. $\frac{8}{3}$
• B. $\frac{4}{3}$
• C. $4$
• D. $0$

Answer 1

The correct option is B $\frac{4}{3}$

Let $P(3,4,5)$ $Q(4,6,3)$ $R(-1,2,4)$ and $S(1,0,5)$ be any four points.

The dr's of the line $PQ$ are $(1,2,-2)$

The dr's of the line $RS$ are $(2,-2,1)$

The projection of $RS$ on $PQ$ will be $RS\times \cos \theta$

$RS\cos \theta$ $=$ $\frac{PQ\times RS}{|PQ|}$

$=$ $\frac{(i+2j-2k).(2i-2j+k)}{3}$ $=$ $\frac{4}{3}$