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(B) The given vector equation is $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$.We can rewrite this as $\ov

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(B) The given vector equation is $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$.We can rewrite this as $\overrightarrow{r} = \overrightarrow{a} - p\overrightarrow{a} - q\overrightarrow{a} + p\overrightarrow{b} + q\overrightarrow{c}$.Rearranging the terms, we get $\overrightarrow{r} - \overrightarrow{a} = p(\overrightarrow{b} - \overrightarrow{a}) + q(\overrightarrow{c} - \overrightarrow{a})$.This is the parametric form of the equation of a plane passing through the point with position vector $\overrightarrow{a}$ and parallel to the vectors $(\overrightarrow{b} - \overrightarrow{a})$ and $(\overrightarrow{c} - \overrightarrow{a})$.Since $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are non-coplanar, the vectors $(\overrightarrow{b} - \overrightarrow{a})$ and $(\overrightarrow{c} - \overrightarrow{a})$ are linearly independent, thus defining a unique plane.

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

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