1. The problem statement, all variables and given/known data Assume that [itex](|v_1>, |v_2>, |v_3>)[/itex] is an orthonormal basis for V. Show that any vector in V which is orthogonal to [itex]|v_3>[/itex] can be expressed as a linear combination of [itex]|v_1>[/itex] and [itex]|v_2>[/itex]. 2. Relevant equations Orthonormality conditions: |v_i>*|v_j> = 0 if i≠j OR 1 if i=j. 3. The attempt at a solution I dont know how to mathematically prove this obvious one. I understand the definitions here. Orthonormal basis implies that the set of three vectors lives in dimension three and are all orthogonal to one another. This means the |v_1> *|v_2> = 0. If some vector is orthogonal to |v_3> that means |x> |v_3> = 0. I am pretty sure we have to use sum notation for an inner product and orthonormality conditions to prove this statement. Hints on starting out properly? Here's the only lead I have: |x> = c*|v_1> + t*|v_2> as it is a linear combination of v_1 and v_2. But we don't want to assume the proof.