If the lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then

Engineering

Mathematics

Equation of Straight Line in 3D and Distance Of a Point From Line

Question

aa' + c + c' = 0

bb' + cc' + 1 = 0

ab' + bc' + 1 = 0

cc' + a + a' = 0

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Line x = ay + b, z = cy + d

$\Rightarrow \frac{x - b}{a} = \frac{y}{1} = \frac{z - d}{c}$

$Line x = a ’ z + b ’, y = c ’ z + d ’$

$\Rightarrow \frac{x - b'}{a'} = \frac{y - d'}{c'} = \frac{z}{1}$

Given both the lines are perpendicular

⇒ aa' + C' + C = 0