Sejam os vetores u=(1,1,0), v=(2,0,1) w1=3u-2v, w2=u+3v w3=(1,1,-2). Determinar o volume do paralelepípedo definido pelos vetores w1, w2 e w3.

Realize os cálculos abaixo:

Volume: w1.(w2 x w3) 

Dessa forma, temos:

w1 = 3u - 2v 
w1 = 3(1,1,0) - 2(2,0,1) 
w1 = (3,3,0) - (4,0,2) 
w1 = (-1,3,-2) 

w2 = u + 3v 
w2 = (1,1,0) + 3(2,0,1) 
w2 = (1,1,0) + (6,0,3) 
w2 = (7,1,3) 

w3 = i + j - 2k 
w3 = (1,1,-2) 

V = w1.(w2 x .w3) 
(w2 x .w3) = (7,1,3) x (1,1,-2) [Produto vetorial] 
(w2 x w3) = (-5,17,6) 
V = w1.(-5,17,6) 
V = (-1,3,-2).(-5,17,6) 
V = (5 + 51 - 12) 
V = 44 u.v