Suppose I'm given $2$ random vectors $(v_1,v_2)$
I want to find orthonormal basis $(w_1,w_2)$
Are the following equivalent? for the $w_2$ case
$$w_1=\frac{v_1}{\|v_1\|}$$ $$x_2=v_2-\frac{(v_1,v_2)}{(v_1,v_1)}v_1$$
or $$x_2=v_2-(v_1,v_2)v_1 $$ or $$x_2=v_2-\frac{(w_1,v_2)}{(w_1,w_1)}w_1$$
or $$x_2=v_2-(w_1,v_2)w_1 $$
and then $$w_2=\frac{x_2}{\|x_2\|}$$