Question

Seja os vetores u=(1,1,0),v=(2,0,1),w1 =3u-2v,w2=u+3v e w3=i+j+2k. Determinar o volume do paralelepípedo definido por w1,w2 e w3

Answer 1

Bom dia Vanusa

u = (1, 1, 0)
v = (2, 0, 1)

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

w2 = u + 3*v 
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) 

Volume

V = w1.(w2 x w3) 
(w2 x w3) = (7,1,3) x (1,1,2) 

i   j  k   i   j
7 1 3   7  1
1 1 2   1  2

2i + 3j+ 14k - k - 3i - 14j = -i - 11j + 13k = (-1,-11,13)

V = w1.(-1,-11,13) 
V = (-1,3,-2).(-1,-11,13) 
V = 1 - 33 - 26 = -58
V = l-58l = 58 u.v