Short Answer TypeFind the length and foot of the perpendicular drawn from the point (3, 4, 5) on the line 
Find the length of the perpendicular drawn from the point (1, ,2 3) on the line
Any point M on this line is
(3 r + 6, 2 r + 7, –2 r + 7)
Let this point M be the foot of perpendicular from P(1, 2, 3) on AB
Direction ratios of PM are
3 r + 6 – 1, 2 r + 7 – 2, – 2 r + 7 – 3 i.e. 3 r + 5, 2 r + 5, – 2 r + 4
Direction ratios of AB are 3, 2, –2
Since PM ⊥ AB
∴ (3 r + 5) (3) + (2 r + 5) (2) + (– 2 r + 4) (–2) = 0
∴ 9 r + 15 + 4 r + 10 + 4 r – 8 = 0
⇒ 17 r = –17 ⇒ r = – 1
∴ M is (3, 5, 9)
∴ required length of perpendicular = PM
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