Diketahui vektor vektor p=(5 -4), vektor q=(3 8), dan

a. -17, b. -34, c. 17, d. -76

Pembahasan

Diketahui vektor p = (5, -4), q = (3, 8), dan r = (-2, 6).
Operasi vektor:
a. Vektor p . vektor q (Hasil kali titik/dot product):
p . q = (px * qx) + (py * qy)
p . q = (5 * 3) + (-4 * 8)
p . q = 15 + (-32)
p . q = 15 - 32
p . q = -17

b. Vektor p . vektor r:
p . r = (px * rx) + (py * ry)
p . r = (5 * -2) + (-4 * 6)
p . r = -10 + (-24)
p . r = -10 - 24
p . r = -34

c. Vektor p . (vektor q - vektor r):
Langkah 1: Hitung (vektor q - vektor r)
q - r = (qx - rx, qy - ry)
q - r = (3 - (-2), 8 - 6)
q - r = (3 + 2, 2)
q - r = (5, 2)

Langkah 2: Hitung p . (q - r)
p . (q - r) = (px * (qx-rx)) + (py * (qy-ry))
p . (q - r) = (5 * 5) + (-4 * 2)
p . (q - r) = 25 + (-8)
p . (q - r) = 25 - 8
p . (q - r) = 17

d. (vektor p - vektor q) . vektor r:
Langkah 1: Hitung (vektor p - vektor q)
p - q = (px - qx, py - qy)
p - q = (5 - 3, -4 - 8)
p - q = (2, -12)

Langkah 2: Hitung (p - q) . r
(p - q) . r = ((px-qx) * rx) + ((py-qy) * ry)
(p - q) . r = (2 * -2) + (-12 * 6)
(p - q) . r = -4 + (-72)
(p - q) . r = -4 - 72
(p - q) . r = -76