Find projection of a vector on a plane

Given a vector V in 3D space and a normal vector N of a plane, how to calculate the projection of V on the plane?

The following is my C++ and OpenCV implementation of the algorithm.

 

Vec3d findProjection(Vec3d V, Vec3d N) {
    Vec3d v, n;
    // We convert both vectors to unit vectors
    normalize(V, v);
    normalize(N, n);
    // Then calculate the cos angle between n and v
    double cosVN = v.dot(n);
    // Make sure the angle is in range of -90 to 90 degrees
    if(cosVN < 0) {
        cosVN = -cosVN;
        n = -n;
    }
    double V_len = sqrt(V.dot(V));
    double _N_len = V_len * cosVN;
    // _N is the projection of V on N
    Vec3d _N = _N_len * n;       
    return V - _N;
}