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

Today, August 18

Question

The line x = ay + b, z = cy + d and x = a¢ y + b¢, z = c¢y + d¢ are perpendicular if –

A

aa¢ + bb¢ + 1 = 0

B

ab¢ + a¢b + 1 = 0

C

aa¢ + bb + cc¢ = dd¢

D

aa¢ + cc¢ + 1 = 0

Answer

aa¢ + bb + cc¢ = dd¢

Explanation

Solution

The equations of straight line can be rewritten as

x = ay + b, z = cy + d

Ž $\frac{x - b}{a}$ = $\frac{y - 0}{1}$ = $\frac{z - d}{c}$ and x = a¢y + b¢, z = c¢y + d¢

Ž $\frac{x - b'}{a'}$ = $\frac{y - 0}{1}$ = $\frac{z - d'}{c'}$

The above lines are perpendicular if aa¢ + 1.1 + cc¢ = 0

Ž aa¢ + cc¢ + 1 = 0.