Question

As retas das equações 3x-y+5=0 e 2x+y+3=0 e formam um ângulo de:
a) 30°
b) 45°
c) 60°
d) 90°
e) 120°

Answer 1

Resposta:

Letra B

Explicação passo-a-passo:

$r:3x~-y+~5~=~0\implies y=3x+5\implies m_{r}=3\\\\2x+~y~+~3~=~0\implies y~=-2x~~-3\implies {m_s} =-2\\\\tg\alpha = |\frac{m_r{-{m_s} } }{1+m_{r}.m_{s} } |\\\\tg\alpha =| \frac{3-(-2)}{1+3.(-2)} |\\\\tg\alpha =|\frac{3+2}{1-6} |\\\\tg\alpha =|\frac{5}{-5}|\\\\tg\alpha =|-1|\\\\tg\alpha =1\implies\alpha = 45^\°$

Answer 2

Resposta:

Letra b

Explicação passo-a-passo:

r:3x −y+ 5 = 0⟹y=3x+5⟹mr=32x+ y + 3 = 0⟹y =−2x  −3⟹ms=−2tgα=∣1+mr.msmr−ms∣tgα=∣1+3.(−2)3−(−2)∣tgα=∣1−63+2∣tgα=∣−55∣tgα=∣−1∣tgα=1⟹α=45\°