Question
Find the perpendicular distance of the point (1, 0, 0) form the line 
Solution
Let the given line AB be
Any point M on this line is (2 r + 1, – 3 r – 1, 8 r – 10)
Let this point M be the foot of perpendicular form P( 1,0, 0) on AB.
Direction ratios of PM are
2 r + 1 – 1, –3 r – 1 – 0,
8 r – 10 – 0 i.e. 2 r, – 3 r – 1, 8 r – 10
Direction-ratios of AB are 2, –3, 8
Since PM ⊥ AB
∴ (2 r) (2) + (– 3r – 1) (–3) + (8 r – 10) (8) = 0
∴ 4 r + 9 r + 3 + 64 r – 80 = 0
∴ 77 r = 77 ⇒ r = 1
∴ M is (3, –4, –2)
Required distance = PM = 
