If the line x = ay + b, z = cy + d and the line z = a¢y + b... | MATH - LINE | SolveeIt | Solveeit

Today, August 18

Question

If the line x = ay + b, z = cy + d and the line

z = a¢y + b¢, z = c¢y + d¢ are perpendicular, then–

A

aa¢ + cc¢ = –1

B

aa¢ + bb¢= 1

C

aa¢ + bb¢ = 0

D

None of these

Answer

aa¢ + cc¢ = –1

Explanation

Solution

Equations of lines can be written as

$\frac{x - b}{a}$ = $\frac{y}{1}$ = $\frac{z - d}{c}$ and $\frac{x - b'}{a'}$ = $\frac{y}{1}$ = $\frac{z - d'}{c'}$

These lines are perpendicular if aa¢ + 1.1 + cc¢ = 0

So aa¢ + cc¢ = –1