Question

Encontre o ponto P no segmento (AB) de tal forma que (AP) = 2(PB) ⃗,onde A = (0, 1, 2) e B = (2, 1 ,4).

Answer 1

AP = 2PB

P-A = 2(B-P)

(a,b,c) - (0,1,2) = 2[(2,1,4) - (a,b,c)]

(a,b-1,c-2) = 2(2-a,1-b,4-c)

(a,b-1,c-2) = (4-2a,2-2b,8-2c)

a = 4-2a
a+2a = 4
3a = 4
a = 4/3

b-1 = 2-2b
b+2b = 2+1
3b = 3
b = 1

c-2 = 8-2c
c+2c = 8+2
3c = 10
c = 10/3

P = ( 4/3, 1 ,10/3 )