Question

Calcule o ângulo entre as retas R: x + √3y=1 S: {x= -t -1 {Y =√3t?

Answer 1

Oi Samuel

r: x + √3y = 1

s:

x = -t - 1
y = √3t 

t = -1 - x
y = √3*(-1 - x) = -√3x - √3

r: x + √3y = 1
√3y = 1 - x
y = (1 - x)/√3
mr = -√3/3 

s: y = -√3x - √3
ms = -√3

tg(α) = |(mr- ms) / (1 + mr*ms)|

tg(α) = |(-√3/3 + √3) / (1 + (-√3/3*-√3)|

tg(α) = 1/2*(√3 - 1/√3) = 1/2*(3 - 1)/√3 = 1/√3 = √3/3 

α = 30°

.