diketahui vektor vektor a=(1 2 -3) b=(4 4 m) dan c=(3 -4 5) jika vector a tegak lurus vektor b hasil dari a+b-2c=

Mapel : Matematika
Kelas : X SMA
Bab : Vektor

Pembahasan :
Syarat tegak lurus
a . b = 0
[1 2 -3] . [4 4 m] = 0
1.4 + 2.4 + (-3)m = 0
4 + 8 - 3m = 0
3m = 12
m = 12/3
m = 4

Maka...
a + b - 2c
= [1 2 -3] + [4 4 m] - 2[3 -4 5]
= [1 2 -3] + [4 4 4] - [6 -8 10]
= [-1 14 -9]
= -i + 14j - 9k

a ⊥ b, maka
a . b = 0
(1,2,-3) . (4,4,m) = 0
4 + 8 - 3m = 0
-3m = -12
m = 4

a + b - 2c
= (1,2,-3) + (4,4,4) - 2(3,-4,5)
= (1,2,-3) + (4,4,4) - (6,-8,10)
= (-1,14,-9)