C++ programming to find an orthonormal basis for R^n

Given K vectors in n-dimensions, i.e. V={v_1, v_2, ..., v_k} in R^n, such that they are orthogonal to each other and k<n. Find a set of (n-k) vectors that form an orthonormal basis for R^n along with V. The problem can also be re-stated as find an orthonormal basis of the null space of a matrix of dimension, k*n. You can use the concept given here or any other concept as you like, [login to view URL] We cannot use any libraries, all codes have to be written and must be in C++ and must be in basis C++ like using functions, arrays, etc.