C++ – Canonical form of += operator for classes

I know that it's a good idea to make as much of the interface of a class non-member non-friend as possible, and I've just realised that for my 3D vector class, 'Vector3', I can move the +=, -= and so on operators out of the class, leaving just constructors and the copy assignment operator.

The question is: what should this operator look like? I've seen canonical forms of plenty of other operators and have followed their advice, but I haven't seen canonical forms of these operators. I've given what I think it should be below.

The secondary question is: what are these operators even called? Arithmetic assignment operators?

The (relevant) code before:

class Vector3 {
public:
    Vector3& operator+=(const Vector3& rhs);
    float x, y, z;
};

Vector3& Vector3::operator+=(const Vector3 &rhs) {
    x += rhs.x;
    y += rhs.y;
    z += rhs.z;

    return *this;
}

What I've changed it to so far:

class Vector3 {
public:
    float x, y, z;
};

Vector3& operator+=(Vector3& lhs, const Vector3& rhs) {
    lhs.x += rhs.x;
    lhs.y += rhs.y;
    lhs.z += rhs.z;

    return lhs;
}