Diketahui vektor a : 4i - 3j -5k vektor b : -5i - 2j+k dan c : 2i-j-k tentukan a : 2a +b - c , b |2a +b + c| mohon bantuannya kak

a = (4 , -3 , -5)
b = (-5 , -2 , 1)
c = (2 , -1 , -1)

a)
...2a + b - c
= 2(4 , -3 , -5) + (-5 , -2 , 1) - (2 , -1 , -1)
= (8 , -6 , -10) + (-5 , -2 , 1) + (-2 , 1 , 1)
= (1 , -7 , -8)

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

|2a + b + c|^2 = 5^2 + (-9)^2 + (-10)^2
|2a + b + c|^2 = 25 + 81 + 100
|2a + b + c|^2 = 206
|2a + b + c| = akar 206

Mapel : Matematika
Kelas : XII SMA
Bab : Vektor

Pembahasan :
A||

2a + b - c
= 2[4 -3 -5] + [-5 -2 1] - [2 -1 -1]
= [8 -6 -10] + [-5 -2 1] - [2 -1 -1]
= (8 - 5 - 2)i + (-6 - 2 + 1)j + (-10 + 1 + 1)k
= i - 7j - 8k
= [1 -7 -8]

B. |2a + b + c| = √[(-1)² + (-7)² + (-8)²]
|2a + b + c| = √[1 + 49 + 64]
|2a + b + c| = √114