Question

Determine K para que as retas L1 2x=3y-5=0 e L2 = K2- 2y=4=0 sejam perpendiculares. 

Answer 1

$L_1=2x+3y-5=0 \\ \\ m_{L_1}=-\frac{2}{3} \\ \\ L_2: 2kx-2y+4=0 \\ \\ m_{L_2}=\frac{-2k}{-2}=k$

Para que sejam perpendiculares:

$m_{L_1}.m_{L_2}=-1 \\ \\ -\frac{2}{3}.k=-1 \\ \\ 2k=3 \\ \\ \boxed{k=\frac{3}{2}}$