Diketahui vektor u=(3, t, 1) dan v=(4, 5, 2). Jika proyeksi skalar orthogonal u pada v = (4√5) / 15, maka t=…

jawaban sudah terlampir.

u = (3 , t , 1)
v = (4 , 5 , 2)
u.v = (3 , t , 1) . (4 , 5 , 2)
= 3×4 + t×5 + 1×2
= 12 + 5t + 2
= 5t + 14
|v| = akar [4^2 + 5^2 +2^2]
= akar [16 + 25 + 4]
= akar 45
= akar [9 × 5]
= 3 akar 5
proyeksi skalar orthogonal u pada v

u.v
_____ = (4 akar 5)/15
v

5t + 14
________ = (4 akar 5)/15
3 akar 5

[5t + 14] × 15 = [4 akar 5]×[3 akar 5]
75t + 210 = 60
75t = 60 - 210
75t = - 150
t = - 150/75
t = - 2
Maka t = - 2