Let $\lbrace \mathbf{u_1}, \mathbf{u_2}, \mathbf{u_2} \rbrace$ be an orthonormal basis for an inner product space $V$. Suppose

$$\mathbf{v} = a \mathbf{u_1} + b \mathbf{u_2} + c \mathbf{u_3}$$

is so that $||\mathbf{v}|| = \sqrt{40}$, $\langle \mathbf{v},\mathbf{u_2} \rangle = -6$, and $\langle \mathbf{v}, \mathbf{u_3} \rangle = 2$. Find the possible values for $a$, $b$, and $c$.

$a =$ , $b =$ , $c =$