Prove that the line `x=a y+b ,\ z=c y+d\ a n d\ x=a^(prime)y+b^(prime),\ z=c^(prime)y+d^(prime)` are perpendicular if `aa^(prime)` +`c c^(prime)`+ 1=0`

Explanation

To prove that the lines given by the equations \( x = ay + b, z = cy + d \) and \( x = a'y + b', z = c'y + d' \) are perpendicular if \( aa' + cc' + 1 = 0 \), we can follow these steps:

### Step 1: Write the equations in parametric form
The first line can be expressed in parametric form as:
\[
\begin{align*}
x &= ay + b \\
z &= cy + d
...