Question

Find the value of 'a', if the straight lines $5x-2y-9=0$ and $ay+2x-11=0$ are perpendicular to each other.

Answer 1

If two lines are perpendicular then
Slope of the first line $\left(m1\right)$ x Slope of the second line $\left(m2\right)=-1$
m1 = $\frac{-5}{-2}$ = $\frac{5}{2}$
m2 = $\frac{-a}{2}$
$\frac{5}{2}$ x $\frac{-a}{2}$ = $-1$
$\frac{5a}{4}$ = $-1$
$-5a=-4$
a=$\frac{-5}{-4}$
a =$\frac{4}{5}$