Question

URGENTEE
Se as retas 2x-3y-1=0 e mx - 2y-6=0 são perpendiculares, então m é igual a?

Answer 1

Considerando as retas "r" e "s" :

$r:2x-3y-1=0\\s:mx-2y-6$

Para as retas serem perpendiculares :

$mr.ms=-1$

Logo :

$r:2x-3y-1=0\\-3y=-2x+1\\y=\frac{2x-1}{3}\\\\mr=\frac{2}{3}$

$s:mx-2y-6=0\\-2y=-mx+6\\y=\frac{mx-6}{2}\\\\ms=\frac{m}{2}$

$mr.ms=-1\\\frac{2}{3}.\frac{m}{2}=-1\\\frac{m}{3}=-1\\\\\boxed{m=-3}$