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  4. The two lines x = ay + b , z = cy + d ; and x = a ' y + b' , z = c ' y + d ' are perpendicular to each other if

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Q. The two lines $x = ay + b , z = cy + d ;$ and $x = a ' y + b' , z = c ' y + d '$ are perpendicular to each other if

Three Dimensional Geometry

Solution:

Equation of lines $\frac{x-b}{a} = \frac{y}{1} = \frac{z-d}{c}$
$ \frac{x-b'}{a'} = \frac{y}{1} = \frac{z-d'}{c'} $
Line are perpendicular
$\Rightarrow aa' + 1+ cc' = 0$