diketahui u=3i + 7j + k, v=4i-2j-k dan w=6i-j-k. panjang vektor u+3v-2w adalah

Mapel : Matematika
Kelas : X SMA
Bab : Vektor

Pembahasan :
u + 3v - 2w
= [3 7 1] + 3[4 -2 -1] - 2[6 -1 -1]
= [3 7 1] + [12 -6 -3] - [12 -2 -2]
= [3 3 0]

|u + 3v - 2w| = √[3² + 3² + 0²]
|u + 3v - 2w| = √[9 + 9 + 0]
|u + 3v - 2w| = 3√2

u = (3,7,1)
v = (4,-2,-1)
w = (6,-1,-1)

u + 3v - 2w
= (3,7,1) + 3(4,-2,-1) - 2(6,-1,-1)
= (3,7,1) + (12,-6,-3) - (12,-2,-2)
= (3,3,0)
|u + 3v - 2w|
= √(3² + 3² + 0²)
= 3√2