Let $v\in\textbf{R}^3$ have norm one. If $\{v_{1},v_{2},v_{3}\}$ is an orthonormal basis for $\textbf{R}^{3}$ and $v = a_{1}v_{1} + a_{2}v_{2} + a_{3}v_{3}$, can we have $|a_{1}| > 3$? Justify the answer.
I think the answer should be no because they are in $\textbf{R}^3$, is that right?