Question

if the straight lines 3x-5y=7 and 4x +ay +9=0 are perpendicular to each other find value of a

Answer 1

according to the if the two lines are perpendicular to each other, then it means that they intersect each other at a point. that means the two are intersecting lines and a have one solution. the condition that should satisfy the intersecting lines is:
a₁/a₂≠b₁/b₂
∴3/4≠-5/a..........(1)

so a can be any no. that can satisfy the equation (1). it can be 2