Basis for a subspace and dimension

Find a basis for the subspace W of R^5 given by...

W = {x E R^5 : x . a = x . b = x . c = 0}, where a = (1, 0, 2, -1, -1), b = (2, 1, 1, 1, 0) and c = (4, 3, -1, 5, 2).

Determine the dimension of W. (as usual, "x . a" denotes the dot (inner) product of the vecotrs x and a).

Please show working, your help is much appreciated.

Re: Basis for a subspace and dimension

can you solve the system of equations:

x_{1} + 2x_{3} - x_{4} - x_{5} = 0

2x_{1} + x_{2} + x_{3} + x_{4} = 0

4x_{1} + 3x_{2} - x_{3} + 5x_{4} + 2x_{5} = 0

that's 3 equations in 5 unknowns. assuming the equations are independent (are your 3 vectors linearly independent?), how many "free variables" will you have? how does this help you choose a basis for W?