Diketahui vektor OA=(-4 3), vektor OB=(r-1 2), dan vektor

a. (3r-51, -27), b. (0, 0)

Pembahasan

Diketahui vektor OA=(-4, 3), vektor OB=(r-1, 2), dan vektor OC=(6, 7).
Kita perlu mendefinisikan vektor u, v, dan p:
u mewakili vektor BA = OA - OB = (-4 - (r-1), 3 - 2) = (-4 - r + 1, 1) = (-3 - r, 1)
v mewakili vektor CB = OB - OC = (r-1 - 6, 2 - 7) = (r - 7, -5)
p mewakili vektor AC = OC - OA = (6 - (-4), 7 - 3) = (6 + 4, 4) = (10, 4)

a. Menentukan 5v - p + 2u:
5v = 5 * (r - 7, -5) = (5r - 35, -25)
2u = 2 * (-3 - r, 1) = (-6 - 2r, 2)

5v - p + 2u = (5r - 35, -25) - (10, 4) + (-6 - 2r, 2)
= (5r - 35 - 10 - 6 - 2r, -25 - 4 + 2)
= (3r - 51, -27)

b. Menentukan p + u + v:

p + u + v = (10, 4) + (-3 - r, 1) + (r - 7, -5)
= (10 - 3 - r + r - 7, 4 + 1 - 5)
= (0, 0)

Jadi, a. 5v - p + 2u = (3r - 51, -27) dan b. p + u + v = (0, 0).