The projection of a line joining (3, 4, 5) and ( 4, 6, 3) on the line joining (-1, 2, 4) and (1, 0, 5) is

Let A= (3, 4, 5), P = (-1, 2, 4), B = (4, 6, 3) and Q=(1, 0, 5) dr's of lineAB are (4- 3), (6-4), (3 -5) = 1, 2,-2 and dr's of line PQ are (1 + 1), (0- 2), (5 -4) = 2, -2, 1 

$\therefore$ dc's of a line PQ=  $=\frac{2}{\sqrt{2^2+(-2{)}^2+1}},\frac{-2}{3},\frac{1}{3}$

$=\frac{2}{3},\frac{-2}{3},\frac{1}{3}$

 $\therefore$   projection of line segment AB on the line PQ is 

$\left|\frac{2}{3}\left(1\right)+\left(\frac{-2}{3}\right)\left(2\right)+\left(\frac{1}{3}\right)(-2)\right|=\frac{4}{3}$