Diketahui vektor-vektor a=(4 -2), b=(2 3), dan c=(6 -1).

a. a+b = (6, 1), |a+b| = sqrt(37); b. 2a-c = (2, -3), |2a-c| = sqrt(13); c. 2a-b+3c = (24, -10), |2a-b+3c| = 26.

Pembahasan

Diketahui vektor-vektor:
a = (4, -2)
b = (2, 3)
c = (6, -1)

a. Komponen vektor kolom dan besar dari a+b:
a + b = (4+2, -2+3) = (6, 1)
Besar vektor a+b = |a+b| = sqrt(6^2 + 1^2) = sqrt(36 + 1) = sqrt(37)

b. Komponen vektor kolom dan besar dari 2a-c:
2a = 2 * (4, -2) = (8, -4)
2a - c = (8-6, -4-(-1)) = (2, -3)
Besar vektor 2a-c = |2a-c| = sqrt(2^2 + (-3)^2) = sqrt(4 + 9) = sqrt(13)

c. Komponen vektor kolom dan besar dari 2a-b+3c:
2a = (8, -4)
3c = 3 * (6, -1) = (18, -3)
2a - b + 3c = (8-2+18, -4-3+(-3)) = (24, -10)
Besar vektor 2a-b+3c = |2a-b+3c| = sqrt(24^2 + (-10)^2) = sqrt(576 + 100) = sqrt(676) = 26

Jadi:
a. a+b = (6, 1), |a+b| = sqrt(37)
b. 2a-c = (2, -3), |2a-c| = sqrt(13)
c. 2a-b+3c = (24, -10), |2a-b+3c| = 26