Diketahui titik A (2,-1,4) B (4,1,3) dan C (2,0,5). Sinus sudut antara AB dan AC adalah

AB = b - a = (4, 1, 3) - (2, -1, 4) = (2, 2, -1)
|AB| = √(2^2 + 2^2 + (-1)^2) = √(4 + 4 + 1) = √9 = 3

AC = c - a = (2, 0, 5) - (2, -1, 4) = (0, 1, 1)
|AC| = √(0^2 + 1^2 + 1^2) = √(0 + 1 + 1) = √2

AB.AC = |AB|.|AC| cos ¢
2(0) + 2(1) + (-1)(1) = 3 . √2 cos ¢
0 + 2 - 1 = 3√2 cos ¢
cos ¢ = 1/(3√2) . √2/√2 = (√2)/6 = sa/mi
=> de = √(6^2 - √2^2) = √(36 - 2) = √34

Sin ¢ = de/mi = √34/6 = 1/6 √34