Chapter 5.1, Problem 31E

Considerthe orthonormal vectors ${\stackrel{\to }{u}}_1,{\stackrel{\to }{u}}_2,\mathrm{...}{\stackrel{\to }{u}}_m$ , in ${ℝ}^n$ ,and an arbitrary vector $\stackrel{\to }{x}$ in ${ℝ}^n$ . What is the relationshipbetween the following two quantities?
$p={\left({\stackrel{\to }{u}}_1\cdot \stackrel{\to }{x}\right)}^2+{\left({\stackrel{\to }{u}}_2\cdot \stackrel{\to }{x}\right)}^2+\cdots +{\left({\stackrel{\to }{u}}_m\cdot \stackrel{\to }{x}\right)}^2$ and ${\Vert \stackrel{\to }{x}\Vert }^2$
When are the two quantities equal?