If $\vec{a}, \vec{b}, \vec{c}$ are three non-coplanar vectors, then the  vector equation $\vec{r}= ( 1- p - q) \vec{a} + p \vec{b} + q\vec{c}$ represents a 

plane 

We have,

$\vec{r} = (1 - p - q) \vec{a} +p \vec{b}+q\vec{c}$

$⇒\vec{r} = \vec{a} + p(\vec{b}-\vec{a}) + q (\vec{c}-\vec{a})$

Clearly, it represents a plane passing through a point having position vector $\vec{a}$ and a parallel to the vectors $\vec{b} - \vec{a}$ and $\vec{c}-\vec{a}$.