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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:

AIEEEAIEEE 2006

Solution:

The equations of given lines are
$x = ay+bjZ = cy + d$
and $x = a'y + b', z = c’y + d’$
These equations can be rewritten as
$\frac{x-b}{a}=\frac{y-0}{1}=\frac{z-d}{c}$
and $\frac{x-b'}{a'}=\frac{y-0}{1}=\frac{z-d'}{c'}$
These lines will perpendicular, if
$aa' + cc' + 1 = 0$