Vektor a = x – j + 2k

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Vektor b = 4i + 2j – 4k
Sudut a & b = 180°

Tentukan nilai x

Vektor a = x – j + 2k

A.b = a1b1+a2b2+a3b3
=4x-2-8
a.b= 4x-10
|a|= akar xkuadrat+(-1)kuadrat+2kuadrat
=akar xkuadrat+5
|b|= akar 4kuadrat+2kuadrat+(-4)kuadrat
= akar 16+4+16
= akar36 = 6

a.b = |a| × |b| cos ø
= akar xkuadrat+5 × 6 cos180°
=akar xkuadrat+5 × 6 × (-1)
= akar xkuadrat+5 ×(-6)
= -6akar xkuadrat+5

a.b=a.b maka

4x-10= -6akar xkuadrat +5

di kuadratkan.

16 xkuadrat – 100 = 36xkuadrat + 180
=36xkuadrat-16xkuadrat +180 +100
=20xkuadrat +280
20xkuadrat = -280
xkuadrat = -280/20
xkuadrat = -14
x = akar -14