Diketahui vektor u=3 hati-4 hatj-4 hatk , vektor v=2

23/13

Pembahasan

Untuk mencari proyeksi skalar ortogonal (u+v) pada w, pertama-tama kita perlu menjumlahkan vektor u dan v:
u + v = (3hati - 4hatj - 4hatk) + (2hati - hatj + 3hatk)
u + v = (3+2)hati + (-4-1)hatj + (-4+3)hatk
u + v = 5hati - 5hatj - hatk

Selanjutnya, kita perlu mencari dot product (u+v) ⋅ w dan panjang vektor w (|w|).
(u+v) ⋅ w = (5hati - 5hatj - hatk) ⋅ (4hati - 3hatj + 12hatk)
(u+v) ⋅ w = (5 × 4) + (-5 × -3) + (-1 × 12)
(u+v) ⋅ w = 20 + 15 - 12
(u+v) ⋅ w = 23

|w| = sqrt(4² + (-3)² + 12²)
|w| = sqrt(16 + 9 + 144)
|w| = sqrt(169)
|w| = 13

Proyeksi skalar ortogonal (u+v) pada w adalah:
Proyeksi = [(u+v) ⋅ w] / |w|
Proyeksi = 23 / 13