If the lines $x = ay + b, z = cy + d $ and $ x = a'y + b', z = c'y+ d'$ are perpendicular, then
Answer & explanation
Correct answer: option 2
The correct answer is Option 2: $aa' + cc' = -1 $
The equation of the given lines are not in symmetrical form. We first put them in symmetrical form.
Equations of first line are $ x = ay + b, z = cy + d.$ These equations can be written as
$\frac{x-b}{a}=y, \frac{z-d}{c}=y ⇒\frac{x-b}{a}=\frac{y-0}{1}=\frac{z-d}{c}$...........(i)
Similarly, $ x = a' y + b' , z = c' y + d'$ can be written as
$\frac{x-b'}{a}=\frac{y-0}{1}=\frac{z-d'}{c}$ .......(ii)
If line (i) and (ii) are per perpendicular, then
$aa' + 1 + cc' = 0 ⇒ aa' + cc' = - 1 $