Question

Hi! I have one question that I just can't figure out.

If vector A = (6.00 i -8.00 j) units, vector B = (-8.00 i + 3.00 j) units, and vector C = (25.0 i + 22.0 j) units, determine a and b such that a vector A + b vector B + vector C= 0.

Answer 1

a(6i - 8j) + b(-8i + 3j) + (25i + 22j) = 0

Group the components
(6a - 8b + 25)i + (-8a + 3b + 22)j = 0i + 0j

Now there's a system of equations
6a - 8b + 25 = 0
-8a + 3b + 22 = 0

Answer 2

Ah, now I see. I forgot to factor out the i's and j's, so I was rather confused :3
Thank you!