Resolução Produto Vetorial.pdf

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Exercício 1. Calcule o produto vetorial u x u para: 
a) u = (5,4,3) e v = (1,0,1); 
b) u = (3, 1,2) e v = (-2,2.5); 
c) u = (1,-1, 1) e v = (2,-3,4); 
d) u = (1, -2, -2) e v = (2,0, -1); 
e) u = (2, 1,-1) e v = (1,-1,3). 
 
Exercício 2. Se u = (3, -1, -2), v = (2,4, -1) e w = (-1,0,1), determine: 
a) lu x vl; 
b) (2v) x (3v); 
c) (u x w) + (w x u); 
d) (u x v) x (v x u); 
e) (u - v) x w; 
f) (u x v) x w; 
g) u x (v x w); 
h) u x (v + w); 
i) u x v + u x w; 
j) ⟨u x v, v⟩; 
k) ⟨u x v, w⟩; 
l) ⟨u,v x w⟩. 
 
RESPOSTAS 
 
Ex.1: 
a) (4,-2,-4) b) (1,-19.8), c) (-1.-2.-1), 
d) (2,-3,4), e) (2,-7,-3). 
 
Ex.2: 
a) √278 b) (0,0,0), c) (0,0,0), d) (0,0,0), 
e) (-5,0,-5) f) (-1,-23,-1) g) (-6,-20,1) h) (8,-2,13), 
i) (8,-2,13) j) 0 k) 5 l) 5