If →a,→b and →c determine the vertices of a triangle, show that 12[→b×→c+→c×→a+→a×→b] gives the vector area of the triangle. Hence, deduce the condition that the three points →a,→b and →c are collinear. Also, find the vector normal to the plane of the triangle.

If →a,→b and →c determine the vertices of a triangle, show that

1.	If →a,→b and →c determine the vertices of a triangle, show that 12[→b×→c+→c×→a+→a×→b] gives the vector area of the triangle. Hence, deduce the condition that the three points →a,→b and →c are collinear. Also, find the vector normal to the plane of the triangle.
Answer» If $\to a, \to b a n d \to c$ determine the vertices of a triangle, show that $\frac{1}{2} [\to b \times \to c + \to c \times \to a + \to a \times \to b]$ gives the vector area of the triangle. Hence, deduce the condition that the three points $\to a, \to b a n d \to c$ are collinear. Also, find the vector normal to the plane of the triangle.