Question

Achar a distância entre as retas abaixo

Answer 1

Resposta:

(x,y,z)=(2,3,1)+t*(-1,1,-2)

(x,y,z)=(0,-1,0) +t*(1,-3,2)

d(r1,r2)=|[AB,r,s]|/|r x s |

AB=(0-2 , -1-3 , 0-1)=(-2,-4,-1)

r x s =

x   y   z   x    y

-1   1  -2  -1    1

1  -3   2   1   -3

det=2x-2y+3z+2y-6x-z

det=-4x+2z==>r x s = (-4,0,2)

[AB,r,s] = AB . (r x s)

[AB,r,s] = (-2,-4,-1) . (-4,0,2)

[AB,r,s] =8-0-2=6

d(r1,r2)= 8/√[(-4)²+0²+2²]

d(r1,r2)= 8/√(16+4) =8/2√5  unid. de distância