Let $$f(x)=.5x^TQx-b^Tx$$ Let $x_1$ min f for a subspace $B_1$ and $x_2$ min f for a subspace $B_2$ and let $d$ be in both subspaces.
a) Show that there exists a vector $d_1$ which is Q-conjugate to $d$, and such that $x_1$ belongs to the plane spanned by $d$ and $d_1$.
Q-conjugate means the $d^TQd_1=0$. I am not sure how to approach this problem I tried many different things for $d$ and just keep guessing and going nowhere with it.