(Sorry for any misspelling or gramatical error, I´m not a native english speaker)
I am trying to solve this problem:
Vector $u=\begin{bmatrix}a &a &a &b \end{bmatrix}´$ can be written as $u=v+w$ where $v$ and $w$ are not null vectors and are orthogonal and $$|(s-e_{1})´v|=||s-e_{1}||\cdot ||v||$$ with $s=\begin{bmatrix}1 &1 &1 &1 \end{bmatrix}´$. Determine $v$ and $w$ in terms of $a$ and $b$.
What does $e_{1}$ means? The course just started last week but I couldn´t go to class because I was sick. Maybe it´s some kind of notation I don´t know because I didn´t go to class. The problem isn´t from a book (I think), it was in a PDF uploaded in Canvas. I´ve already sent an email asking the same question to my teacher but he doesn´t responds and I continue to be sick so there is no way to ask my teacher.
PD: I´m not asking for the solution of the problem, just for the meaning of $e_{1}$. Please don´t "spoil me" the answer.