Ortho Normalize Proof

using UnityEngine;
using System.Collections;

public class TangentDemo : MonoBehaviour {
    ////////////////////////////////////////////////////////////////////////////////////////////
    // In order to ortho-normalize a vector set,
    //  subtract up the projection of tangent onto the normal and / or binormal from the tangent
    ////////////////////////////////////////////////////////////////////////////////////////////

    void Start () {
        Debug.Log("Up: " + Vector3.up);
        Debug.Log("Right: " + Vector3.right);
        Debug.Log("Forward:  " + Vector3.forward);

        Vector3 up = Vector3.up;
        Vector3 right = Vector3.right;
        Vector3 tangent = up + Vector3.forward;

        Vector3.OrthoNormalize(ref up, ref tangent, ref right);
        Debug.Log("Tangent: " + tangent);
        Debug.Log("---------------------------------");

        up = Vector3.up;
        right = Vector3.right;
        tangent = up + Vector3.forward;

        Vector3 accumulator = Vector3.zero;
        accumulator += up * Vector3.Dot(tangent, up);
        accumulator += right * Vector3.Dot(tangent, right);
        tangent -= accumulator;

        Debug.Log("Tangent: " + tangent);
    }
}