let x and y be vectors such that and compute the ratio ​

let x and y be vectors such that \(\operatorname{proj}_{\mathbf{x}}(\mathbf{y})=\dbinom{5}{3}\)and \(\operatorname{proj}_{\mathbf{y}}(\mathbf{x})=\dbinom{2}{-2}\) compute the ratio \(\dfrac{\|\mathbf{x}\|}{\|\mathbf{y}\|}\)