Question

Dados os pontos A(8,0,-2), B(1,3,-4) e C(-3,-2,2) determine o ponto D tal que AD= BC X AC.

Answer 1

A(8,0,-2), B(1,3,-4) e C(-3,-2,2)

BC=(-4,-5,6)

AC=(-11 ,-2,4)

BC X AC =

x y z x y

-4 -5 6 -4 -5

-11 -2 4 -11 -2

det=-20x-66y+8z+16y+12x-55z =-8x-50y-47z ==>(-8,-50,-47)

Se D=(a,b,c)

AD=(a-8 , b , c+2) = (-8,-50,-47)

a-8 =-8 ==>a=0

b=-50

c+2=-47 ==>c=-49

Ponto D ==> (0,-50,-49)