Question

Soal proyeksi vektor, tolong bantu yah

Answer 1

Verified answer

8 = -8p + 16/√(p² + 16)
8√(p² + 16) = -8p + 16
[8√(p² + 16)]² = (-8p + 16)²
64(p² + 16) = 64p² - 256p + 256
64p² + 1024 = 64p² - 256p + 256
64p² - 64p² + 256p + 1024 - 256 = 0
256p + 768 = 0
256p = -768
p = -3
maaf ya^^ dan terima kasih udah dikoreksi

Answer 2

Verified answer

A = (-2 , -8 , 4)
b = (0 , p , 4)
panjang proyeksi vector a pada vector b
= |c|
= 8

a . b
= (-2)(0) + (-8)(p) + (4)(4)
= 0 + (-8p) + 16
= -8p + 16

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

|c| = a . b / |b|
8 = [-8p + 16]/[V(p^2 + 16)]
8 . V(p^2 + 16) = -8p + 16
V(p^2 + 16) = [8 (-p + 2)]/8
V(p^2 + 16) = -p + 2
p^2 + 16 = (-p + 2)^2
p^2 + 16 = p^2 - 4p + 4
p^2 - p^2 + 4p = 4 - 16
4p = -12
p = -12/4
p = -3

Jadi nilai p adalah -3