Reflection in euclidean space

Homework Statement

V is a three-dimensional euclidean space and v1,v2,v3 is a orthonormal base of that space.
Calculate the Matrix of the reflection over the subspace spanned by v1+v2 and v1+2*v2+3*v3 .

The Attempt at a Solution

To determine the matrix I have first to select a base I could try to use v1,v2,v3 but I can't see how to determine the entries of the matrix then.
I could use v1+v2 and v1+2*v2+3*v3 (the base of the subspace) and try to extend to a base of R^3; however I can't see how to do that with the general case without knowing what v1,v2,v3 actually is.