Question
Find the length and foot of the perpendicular drawn from the point (3, 4, 5) on the line 
Solution
Let the given line AB be 
Any point M on this line is
(2 r + 2, 5 r + 3, 3 r + 1)
Let this point M be the foot of perpendicular from P (3, 4, 5) on AB
Direction-ratios of PM are
2 r + 2 – 3, 5 r + 3 – 4, 3 r + 1 – 5
i.e. 2 r – 1, 5 r – 1, 3 – 4
Direction-ratios of AB are 2, 5, 3
Since PM ⊥ AB
Required length of perpendicular = PM
