Magnitudes y vectores - 2 Vectores 19

Vectores 19. Sean los vectores: A = (3; 2; 1) B = (1; 0; –1) C = (0; –2; 4); calcular cuando corresponda.

a) B x C

B = (1; 0; –1) C =(0; –2; 4)

B x C = (1; 0; –1) x (0; –2; 4)  =

B x C = (( 0 * 4 – (–1) * (–2)) ; ((–1) * 0 –1 * 4 ); (1 * (–2) – 0 * 0 ) )

B x C = -2 î -4 ĵ -2 k  = (-2; -4; -2)

b) –4(B x B) – A

B = (1; 0; –1) A =(3; 2; 1)

B x B = (1; 0; –1) x (1; 0; –1) =

| B x B | = | B | . | B | sen 0 = 0 ------  >   = ( 0 ; 0; 0 )

–4(B x B) = -4 ( 0 ; 0; 0 ) = ( 0 ; 0; 0 )

–4(B x B) – A = ( 0 ; 0; 0 ) - (3; 2; 1) = -3 î -2 ĵ -1 k = (-3; -2; -1)

c) (A + B) x C

A =(3; 2; 1) B = (1; 0; –1) C =(0; –2; 4)

A + B = (3; 2; 1) + (1; 0; –1) = ( 4 ; 2 ; 0 )

(A + B) x C = ( 4 ; 2 ; 0 ) x (0; –2; 4) =

(A + B) x C = (2 * 4 – 0 * (–2)) î+ (0 * 0 – 4 * 4) ĵ+ (4 * (–2) – 2 * 0) k

(A + B) x C =  8 î -16 ĵ -8 k = (8; -16; -8)