Mathematics

The key is to use the perpendicularity and unit-length constraints to set up an equation you can solve for $|\mathbf{x}|^2$. Take the dot product of both sides of the equation with itself—this converts the vector equation into a scalar one. Since $\alpha$ and $\beta$ are perpendicular unit vectors, their dot and cross products have special properties that will simplify nicely and let you isolate $|\mathbf{x}|^2$.

The key is to use the perpendicularity and unit-length constraints to set up an equation you can solve for $|\mathbf{x}|^2$. Take the dot product of both sides of the equation with itself—this converts the vector equation into a scalar one. Since $\alpha$ and $\beta$ are perpendicular unit vectors, their dot and cross products have special properties that will simplify nicely and let you isolate $|\mathbf{x}|^2$.