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Prévia do material em texto

1) Dados os vetores )4,1,1()1,3,2( −=−−= →→
veu, calcular: 
a) ).(2 →→
− vu b) )2).(3( →→→→
−+ uvvu c) )).(( →→→→
−+ vuvu d) )).(( →→→→
−+ uvvu 
(A) 2u . (-v) = - 2(2,-3,-1)(1,-1,4)==>-2(2.1,-3.(-1),(-1).4)
 2(2,3,-4) ==> (4, 6, - 8 ) 
===============================================
(B) (u + 3v) . (v – 2u) = u.v + - 2u² + 3v² - 6uv ==> - 2u² + 3v² - 5uv
-2(2,-3,-1)² + 3(1,-1,4)² - 5(2,-3,-1)(1,-1,4)
-2(4,9,1) + 3(1,1,16) -5(2,3,-4) ==>( - 8,- 18, - 2 )+( 3, 3, 48)-( 10, 15, - 20)
==> ( - 15, 0, 66 ) 
==================================================== (C) (u + v )* (u - v ) = u² - v² ==> (4,9,1)-(1,1,16) ==> (3, 8, - 15)====================================================
(D) (u +v )* (v - u) = -( u² - v²) ==> (4,9,1)-(1,1,16)
-(3, 8, - 15)==> (- 3, - 8, 15 )