The two lines x = a y + b , z = c y + d and x = a ' y + b ' , z = c ' y + d ' will be perpendicular, if and only if:

Question

The two lines $x = a y + b, z = c y + d$ and $x = a' y + b', z = c' y + d'$ will be perpendicular, if and only if:

Smart Achievers · Accepted Answer

(1)

Ans. $a a' + c c' + 1 = 0$

Explanation:

$x = a y + b$

$\Rightarrow$ $y = \frac{x - b}{a}$

$z = c y + d$

$\Rightarrow$ $y = \frac{z - d}{c}$

$\frac{x - b}{a} = \frac{y}{1} = \frac{z - d}{c}$ $\dots (i)$

Similarly, $\frac{x - b'}{a'} = \frac{y}{1} = \frac{z - d'}{c'}$ $\dots (i i)$

Lines are perpendicular so the sum of corresponding product of their dr's be zero. So for perpendicularity of lines, $a a' + 1 + c c' = 0 .$

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