Vectors on a Plane?

Given a=2i+3j, b=3i+5j and c=8i+11j express c in the form ra+sb where r and s are scalars.





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Vectors on a Plane?
ra + sb = r(2i+3j) + s(3i+5j)





distribute and regroup i's and j's, we get





i(2r+3s) + j(3r+5s)





Since c = ra+sb,





2r + 3s = 8


3r + 5s = 11





Solving these, we get r=47/2 and s=-13, so





c = (47/2) a - 13 b

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