Question

Dados os vetores ü=(2,-3,-l) e v=(l,-1,4), calcular:

a) 2ü·(-v)
b) (ü+3v)·(v-2ü)
e) (ü+v)·(Ü-v)
d) (ü+v)·(v-ü)​

Answer 1

Resposta:

u= (2,-3,-1) e v = (1,-1,4), calcular

(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 )