Question

Dados os vetores u=2i-3j+4k , v=3i+2j+k , w = -3i+2k calcule:

a)(2v).(3v)

b)(u.v).(v.u)

c)(u.v).w

d)u.(v.w)

Answer 1

u=2i-3j+4k , v=3i+2j+k , w = -3i+2k

u=(2,-3,4) , v=(3,2,1) e w=(-3,0,2)

a)(2v).(3v) =(4,-6,8).(9,6,3) = 36-48+24 = 12

b)(u.v).(v.u) =[ (2,-3,4) . (3,2,1) ] * [(3,2,1).(2,-3,4)]

=(6-6+4) * ( 6-6+4) = 4 *4=16

c)(u.v).w =[ (2,-3,4) . (3,2,1) ] * (-3,0,2)

=(6-6+4)* (-3,0,2) =4*(-3,0,2) =(-12,0,8)

d)u.(v.w) =(2,-3,4) * [(3,2,1) . (-3,0,2)]

=(2,-3,4) *(-9+0+2)

=(2,-3,4)*(-7) =(-14 ,+21,-28)