Determine the co-ordinates of $x$ =(9, 10, 11), $v_1$ -$4v_2$ and $v_3$ with respect to $v_1, v_2, v_3$.
$v_1$ = ($\frac{1}{3}$,-$\frac{2}{3}$,$\frac{2}{3}$)
$v_2$ = ($\frac{2}{3}$,-$\frac{1}{3}$,-$\frac{2}{3}$)
$v_3$ = ($\frac{2}{3}$,$\frac{2}{3}$,$\frac{1}{3}$)
Basis $\{v_1,v_2,v_3\}$ is orthonormal, so you can find coordinates of a vector in this basis by taking the dot product of the vector and basis vectors, so since $\langle v_1,x\rangle=11/3,\langle v_2,x\rangle=-14/3,\langle v_3,x\rangle=49/3$ coordinates of $x$ in this basis are $(11/3,-14/3,49/3)$, you can find coordinates of $v_1-4v_2$ similarly.