1. The problem statement, all variables and given/known data In real-number multiplication, if uv1 = uv2 and u ≠ 0, then we can cancel the u and conclude that v1 = v2. Does the same rule hold for the dot product: If u • v1 = u • v2 and u ≠ 0, can you conclude that v1 = v2? Give reasons for your answer. 2. Relevant equations 3. The attempt at a solution If we let u = k<u1, u2> with u2 = 0 and scalar k, then the dot product of u with any other vector v = k<v1, v2> will simply be the component kv1 because u2 will make the ku2kv2 product always zero regardless of its value. Thus, v can be infinitely many different vectors and still have the same dot product with u.