Perkalian Vektor1. Perkalian titik antara 2 vektor (skalar) / DOT PRODUCT

A = A x + A y + A z B = B x + B y + B z

. = 1 . 1. = 1 . = 1 . = 1.1Cos 90 = 0 . = 1k . j = 1

Contoh Soal :

A =2 + 3 + 4 2A = 4 + 6 + 8 B = - 5 + 7 C = 3 - 4

A . B = (2.1) + (3(-5) + 4.7 = 2 15 = 28 = 15

(2A + C).B = (7 + 2 + 8 ) . ( - 5 + 7 ) = 7-10+56 = 53

2.Perkalian silang antara 2 vektor / Cross productA x = AB sin A = A x + Ay + Bz

AxB =AxAyAzBxByBz= ( AyBz AzBy ) + ( AzBx-AxBz ) + ( AxBy AyBx ) Contoh Soal :

A = 4 + 3 + B = 3 - 2 + 5 C = 3 - 6

Ditanya a. AxB = ? b. (A+B)xC = ?Jawaba.AxB =4313-25

= ( 3.5-1 (-2) + ( 1.3 4.5 ) + ( 4.(-2) 3.3)= 17 - 17 - 17

b.(A+B)xC = ?(A+B) = 17 - 17 - 17

(A+B)xC = 71620-6 = ( -6+0) + ( 12 + 42 ) + (0-2) = -6 + 54 - 2

Contoh Soal :Resultan kedua vektor besarnya sama dengan masing-masing vektor hitung sudut antara kedua vektor

R = F1 = F2 = FR2 = F11 + F22 + 2F1F2 Cos F2 = 2F2 + 2F2 Cos -F2 = 2F2 Cos - = Cos = 120o

Muhammad Wildan Nasir 18