Question

If the line $x=ay+b,z=cy+d$ and the line $x=a^{\prime }y+b^{\prime },z=c^{\prime }y+d^{\prime }$ are perpendicular then :

• A. $a{a}^{\prime }+c{c}^{\prime }+1=0$
• B. $a{a}^{\prime }+b{b}^{\prime }=1$
• C. $a{a}^{\prime }+b{b}^{\prime }=0$
• D. None of these

Answer 1

Answer: (A)

$a{a}^{\prime }+c{c}^{\prime }+1=0$

The lines are $\frac{x-b}{a}=\frac{y-0}{1}=\frac{z-d}{c}$
and $\frac{x-b^{\prime }}{a^{\prime }}=\frac{y-0}{1}=\frac{z-d^{\prime }}{c^{\prime }}$ are perpendicular
if $a{a}^{\prime }+1+c{c}^{\prime }=0$