proyeksi skalar vektor a=(-2,8,4)pada vektor b=(0,p,4)adalah 8,tentukan nilai p

VEKTOR

a•b = -2×0 + 8×p + 4×4
a•b = 8p + 16

|b| = akar(0^2 + p^2 + 4^2)
|b| = akar(0 + p^2 + 16)
|b| = akar(p^2 + 16)

a•b/|b| = 8
a•b = 8×|b|
8p + 16 = 8 × akar(p^2 + 16)
(8p + 16)^2 = (8 × akar(p^2 + 16))^2
64p^2 + 256p + 256 = 64 ×(p^2 + 16)
64p^2 + 256p + 256 = 64p^2 + 1024
256p = 1024 - 256
256p = 768
p = 768/256
p = 3

jadi p = 3