C = 8i + 6j+ 2k, hitung:
a. A . B,
b. B . C
c. A x C
d. B x A
Jika ada 3 buah vector, Vektor A = 10 i + 7j + 4k dan Vektor B = 9i + 5j + 3k dan Vektor
Dik : A = 10i + 7j + 4k
B = 9i + 5j + 3k
C = 8i + 6j + 2k
Dit : a. A . B = …?
b. B . C = …?
c. A × C = …?
d. B × A = …?
Jawab :
a. A . B
A . B = AxBx + AyBy + AzBz
= 10i(9i) + 7j(5j) + 4k(3k)
= 10(9) + 7(5) + 4(3)
= 90 + 35 + 12
= 125 + 12
= 137
b. B . C
B . C = BxCx + ByCy + BzCz
= 9i(5i) + 5j(6j) + 3k(2k)
= 9(5) + 5(6) + 3(2)
= 45 + 30 + 6
= 75 + 6
= 81
c. A × C
A × C = (AyCz–AzCy)i + (AzCx–AxCz)k + (AxCy–AyCx)k
= [(7.2)-(4.6)]i + [(4.5)-(10.2)]j+ [(10.6)-(7.5)]k
= [(14)-(24)]i + [(20)-(20)]j + [(60)-(35)]k
= (14-24)i + (20-20)j + (60-35)k
= -10i + 0j + 25k
= -10i + 25k
d. B × A
B × A = (ByAz–BzAy)i + (BzAx–BxAz)j + (BxAy–ByAx)k
= [(5.4)-(3.7)]i + [(3.10)-(9.4)]j + [(9.7)-(5.10)]k
= [(20)-(21)]i + [(30)-(36)]j + [(63)-(50)]k
= (20-21)i + (30-36)j + (63-50)k
= 1i + (-6)j + 13k
= i – 6j + 13k