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

$$\begin{gathered} Given points P=(3,4,5),Q=(4,6,3),R=(-1,2,4) and S=(1,0,5) \\ D.r\text{'}s of PQ=(1,2,-2) \\ D.c\text{'}s of PQ=(\frac{1}{3},\frac{2}{3},\frac{-2}{3}) \\ \text{ Now projection of RS on PQ is }\left|l\left(x_2-x_1\right)+m\left(y_2-y_1\right)+n\left(z_2-z_1\right)\right| \\ \text{ Where }l,m,n\text{ are D.c's of }PQ \\ =\left|\frac{1}{3}(1+1)+\frac{2}{3}(0-2)+\left(\frac{-2}{3}\right)(5-4)\right| \\ =\left|\frac{2}{3}-\frac{4}{3}-\frac{2}{3}\right| \\ =\frac{4}{3} \end{gathered}$$