Suppose $v_1, v_2, v_3$ is an orthogonal set of vectors in ${\mathbb R}^5$. Let $w$ be a vector in ${\mathrm{Span}}(v_1, v_2, v_3)$ such that
$v_1 \cdot v_1 = 22, v_2 \cdot v_2 = 25.25, v_3 \cdot v_3 = 16$,
$w \cdot v_1 = 66, w \cdot v_2 = 101, w \cdot v_3 = 48$,
then $w =$$v_1 +$$v_2 +$$v_3 .$