Use Lagrange's method to find the maximum value

Use Lagrange's method to find the maximum value of $<A$*x*, x*$>$ subject to condition $<$*x, x*$> =1$ and $<$*u_1, x**$>=0$ where **u_1 is a non zero vector in $N_{(s_1^2I_n-A^TA)}, s_1$ is the largest singular value of A and $A=A^T \in \mathbb{R}^{n*n})$.

Can anybody please explain me how to proceed with this question?

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