1. a × b × c = (a · c) b − a · b c
Exerc´
ıcio: Demonstre a igualdade acima, considerando os seguintes veto-
res
a = ax ux + ay uy + az uz
ˆ ˆ ˆ
b = bx ux
ˆ
c = cx ux + cy uy
ˆ ˆ
Resolu¸ao :
c˜
ux uy uz
ˆ ˆ ˆ
i)b × c = bx 0 0 = 0ˆx + 0ˆy + bx cy uz
u u ˆ
cx cy 0
ux uy
ˆ ˆ uz
ˆ
ii)a × b × c = ax ay az = ay bx cy ux − ax bx cy uy + 0ˆz = ay cy bx ux −
ˆ ˆ u ˆ
0 0 bx c y
ax bx cy uy = ay cy b − ax bx (c − cx ux ) = (ay cy + ax cx ) b − ax bx c = (a · c) b −
ˆ ˆ
a · b c c.q.d.
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