Diketahui vektor a=(-7 3 5), vektor b=(3 -5 4), dan vektor

a. -2b=(-6, 10, -8), b. 3c=(3, -21, 3), c. a-2b+3c=(2, -28, 16), d. |a-2b+3c|=6√29.

Pembahasan

Diketahui vektor a=(-7, 3, 5), vektor b=(3, -5, 4), dan vektor c=(1, -7, 1).

a. -2b
-2b = -2 * (3, -5, 4)
-2b = (-2*3, -2*(-5), -2*4)
-2b = (-6, 10, -8)

b. 3c
3c = 3 * (1, -7, 1)
3c = (3*1, 3*(-7), 3*1)
3c = (3, -21, 3)

c. a - 2b + 3c
a - 2b + 3c = (-7, 3, 5) - (-6, 10, -8) + (3, -21, 3)
a - 2b + 3c = (-7 - (-6) + 3, 3 - 10 + (-21), 5 - (-8) + 3)
a - 2b + 3c = (-7 + 6 + 3, 3 - 10 - 21, 5 + 8 + 3)
a - 2b + 3c = (2, -28, 16)

d. |a - 2b + 3c|
|a - 2b + 3c| = |(2, -28, 16)|
|a - 2b + 3c| = sqrt(2^2 + (-28)^2 + 16^2)
|a - 2b + 3c| = sqrt(4 + 784 + 256)
|a - 2b + 3c| = sqrt(1044)
|a - 2b + 3c| = sqrt(36 * 29)
|a - 2b + 3c| = 6 * sqrt(29)