Representatives of vectors \(\textbf{u}\), \(\textbf{v}\), \(\textbf{p}\), \(\textbf{q}\), and \(\textbf{r}\) are shown in the standard \((x,y)\) coordinate plane below.

One of the following vectors is equal to the vector \(\textbf{u}+\textbf{v}\). Which one?

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First, lets find the components of \(\textbf{u}\) and \(\textbf{v}\).

$$ \textbf{u} = \lang 1,2 \rang $$ $$ \textbf{v} = \lang 1,-1 \rang $$

Adding the components:

$$ \textbf{u}+\textbf{v} = \lang 1+1, 2+(-1) \rang $$ $$ \textbf{u}+\textbf{v} = \lang 2, 1 \rang $$

This corresponds to \(\boxed{\textbf{q}}\).