Let $\lbrace \mathbf{u}_1, \mathbf{u}_2, \mathbf{u}_3 \rbrace$ be an orthonormal basis for an inner product space $V$. If

$$\mathbf{v} = a \mathbf{u}_1 + b \mathbf{u}_2 + c \mathbf{u}_3$$

is so that $\|\mathbf{v}\| = 26$, $\mathbf{v}$ is orthogonal to $\mathbf{u}_3$, and $\langle \mathbf{v},\mathbf{u}_2 \rangle = -26$, find the possible values for $a$, $b$, and $c$.

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