Question

Verifique se as retas r1 e r2 são concorrentes, caso afirmativo, determine o
ponto I(x, y, z).

a) r1: x = 3 + ℎ
y = 1 + 2ℎ
z = 2 − ℎ

r2: x = 5 + 3t
y = −3 − 2t
z = 4 + t

Answer 1

x1=x2
3+h=5+3t
h=5-3+3t
h=2+3t

y1=y2
1+2*(2+3t)=-3-2t
1+4+6t=-3-2t
8t=-8
t=-8/8
t=-1

z1=z2
2-h=4-1
-h=3-2
-h=1 *(-1)
h=-1

t=-1 e h=-1 portanto r1 e r2 são concorrentes.

p(x,y,z)=(5+3t,-3-2t,4+t)

P(2,-1,3)