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