Question

Lines mx + 3y + 7 = 0 and 5x – ny – 3 = 0 are perpendicular to each other. Find the relation connecting m and n.

Answer 1

mx + 3y + 7 = 0

3y = – mx − 7

`y = (-mx)/3 - 7/3`

Slope of this line = `(-m)/3`

5x − ny − 3 = 0

ny = 5x − 3

`y = (5x)/n - 3/n`

Slope of this line = `5/n`

Since, the lines are perpendicular; the product of their slopes is −1.

∴ `((-m)/3)(5/n) = -1`

5m = 3n