If $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}$ are three…
If $\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}, \overrightarrow{\mathbf{c}}$ are three non-coplanar vectors, then the vector equation $\overrightarrow{\mathbf{r}}=(1-p-q) \overrightarrow{\mathbf{a}}+p \overrightarrow{\mathbf{b}}+q \overrightarrow{\mathbf{c}}$ represents a :
straight line
plane
plane passing through the origin
sphere
Solution
We have,
$\overrightarrow{\mathbf{r}}=(1-p-q) \overrightarrow{\mathbf{a}}+p \overrightarrow{\mathbf{b}}+q \overrightarrow{\mathbf{c}}$
where $p, q$ are scalars.
It represents an equation of the plane.