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(B) Given the vector equation $r = (1 - p - q)a + pb + qc$. We can rewrite this as $r = a - pa - qa + pb + qc$. Rearranging the terms,we get $r = a +

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(B) Given the vector equation $r = (1 - p - q)a + pb + qc$. We can rewrite this as $r = a - pa - qa + pb + qc$. Rearranging the terms,we get $r = a + p(b - a) + q(c - a)$. This equation is in the form $r = a + p(b - a) + q(c - a)$,where $p$ and $q$ are scalar parameters. This represents a plane passing through the point with position vector $a$ and parallel to the vectors $(b - a)$ and $(c - a)$. Since $a, b, c$ are non-coplanar,the vectors $(b - a)$ and $(c - a)$ are linearly independent,confirming that the equation represents a plane.

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

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