Mathematics

Problem

Let

\mathbf{x}

and

\mathbf{y}

be vectors such that

\text{proj}_{\mathbf{x}}(\mathbf{y}) = \begin{pmatrix} 5 \\ 3 \end{pmatrix}

and

\text{proj}_{\mathbf{y}}(\mathbf{x}) = \begin{pmatrix} 2 \\ -2 \end{pmatrix}

. Compute the ratio

\frac{\|\mathbf{x}\|}{\|\mathbf{y}\|}