Question

(CESGRANRIO) Se as retas x + 2y + 3 = 0 e ax + 3y + 2 = 0 são perpendiculares, então o parâmetro "a" vale:

-2
2
-6
6
-3

Answer 1

$\large\boxed{\begin{array}{l}\sf r:x+2y+3=0\\\sf 2y=-x-3\\\sf y=-\dfrac{1}{2}x-\dfrac{3}{2}\\\sf m_r=-\dfrac{1}{2}\\\sf s: ax+3y+2=0\\\sf 3y=-ax-2\\\sf y=-\dfrac{a}{3}x-\dfrac{2}{3}\\\sf m_s=-\dfrac{a}{3}\\\sf m_r\cdot m_s=-1\\\sf -\dfrac{1}{2}\cdot-\dfrac{a}{3}=-1\\\sf\dfrac{a}{6}=-1\\\sf a=6\cdot(-1)\\\sf a=-6\end{array}}$