Thread: Finding two subvectors of E, when E is in R3

Im not too certain at all how to solve this example problem I need to figure out to grasp this stuff. Here it is, your help is much appreciated.

Let "E be contained in R^3" be the set of all vectors (x,y,z) such that x + 2y + 3z = 0. Find two vectors v,w in E such that:

E = { av + bw | a, b in R}

note: "be contained in" is my way of typing that sideways U symbol, in which the open end points towards R^3. Thanks!

So, what exactly do you think the problem is asking? And what ideas have you had so far?