Sendo A = (2, 0, 1) B = (0, 3, -2) e C = (1, 2, 0), determinar D, tal que: (BD) ̅ = ( AB ) ̅+ (CB) ̅

Seja \(A = (2, 0, 1), B = (0, 3, -2), C = (1, 2, 0), D = (a,b,c)\)

Vamos determinar cada vetor :

\(AB= B-A= ( 0,3,-2)-(2,0,1)=(-2,3,-3)\\ CB= C-B = (0,3,-2)-(1,2,0)=(-1,1,-2)\\ BD= D-B= (a,b,c)-(0,3,-2)= ( a, b-3, c+2)\)

Assim:

 \((BD) = ( AB ) + (CB)\\ ( a, b-3, c+2)=(-2,3,-3)+(-1,1,-2)\\ ( a, b-3, c+2)= (-3, 4, -5)\)

\(a=-3\\ b-3=4 \rightarrow b= 7\\ c+2=-5 \rightarrow c=-7\)

Assim, o vetor \(D= ( -3,7,-7)\)

Portanto, a alternativa correta é a alternativa B.