1. The problem statement, all variables and given/known data If Avec = (6.00 ihat -8.00 jhat) units, Bvec = (-8.00 ihat + 3.00 jhat) units, and Cvec = (26.0 ihat + 22.0 jhat) units, determine a and b such that a Avec + b Bvec + Cvec= 0. a= b= 2. Relevant equations Avec + Bvec = Rvec Rvec = (Ax + Bx)i-hat + (Ay + By)j-hat 3. The attempt at a solution I tried this two ways. The first way was to isolate one of the variables in terms of the i-hat, and then plug it into the equation for the other variable. So, for instance, doing aAx + bBx + Cx = 0, putting in the numbers to get 6a + (-8b) + 26 = 0. If I proceed algebraically I wind up with values for a and b which make i-hat or j-hat =0, but my understanding of these types of problems is not sufficient to really know how to proceed from there. Would it be assumed to be a given that the value for a in terms of i-hat and the value for a in terms of j-hat which make their separate equations zero must be synonymous with one-another? It's the two dimensions of the vectors which are tripping me up, now.