1. ## Proof with vectors

hi,

I've the following proof with vectors that I don't know how to prove it. Can anyone help me?

1 - The problem is:

For which alpha belongs R, does alpha(1,1,1)^T - (3,2,4)^T have length sqroot(6)?

R - is the real numbers domain.
The matrix showed are transposed.
alpha - is the greek letter

2 - How do I put math characters in the posts?

Thanks,
Pedro

2. $
\alpha \left[ \begin{gathered}
1 \hfill \\
1 \hfill \\
1 \hfill \\
\end{gathered} \right] - \left[ \begin{gathered}
3 \hfill \\
2 \hfill \\
4 \hfill \\
\end{gathered} \right] = \left[ \begin{gathered}
\alpha - 3 \hfill \\
\alpha - 2 \hfill \\
\alpha - 4 \hfill \\
\end{gathered} \right]$
$\;\&\;\sqrt {\left( {\alpha - 3} \right)^2 + \left( {\alpha - 2} \right)^2 + \left( {\alpha - 4} \right)^2 } = \sqrt 6$