Ans=A

We notice that if we add the first two relations together, the vector b will cancel:

(a − b) + (a + b) = (2c) + (4c)

which gives:

2a = 6c        =⇒        a = 3c

and we can use the last of the given equations to substitute for c; we get a = 3c = 3(3i + 4j) = 9i + 12j

Then we can rearrange the first of the equations to solve for b: b   =   a − 2c = (9i + 12j) − 2(3i + 4j)

=   (9 − 6)i + (12 − 8)j

=   3i + 4j

So we have found:

Answer a = 9i + 12j         and       b = 3i + 4j