Question

Determine o angulo entre os planos


π 1: x= -2-2t
y= 1+t-4h
z= -3t-4h


π2: x+y-4=0

Answer 1

π₁: x=-2+0h-2t →(x, y, z)=(-2,1,0)+t(-2,1,-3)+h(0,-4,-4)

y=1-4h+t

z=0-4h-3t

n₁=(-2,1,0)

π₂: x+y+0z-4→n₂=(1,1,0)

$\theta=\frac{n1.n2}{||n1||.||n2||}$

$\theta=\frac{(-2,1,0).(1,1,0)}{\sqrt{{(-1)}^{2}+{1}^{2}+{0}^{2}} .\sqrt{{1}^{2}+{1}^{2}+{0}^{2}}}$

$\theta=\frac{-2+1}{\sqrt{2}.\sqrt{2}}$

$\theta=-\frac{1}{2} \\ \theta=120$