Question

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

• A. $cc' + a + a' = 0$
• B. $aa' + c + c' = 0$
• C. $ab' + bc' + 1 = 0$
• D. $bb' + cc' + 1 = 0$

Answer 1

Answer: (B)

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
$ \Rightarrow aa' +c' +c =0 $