If `veca,vecbandvecc` determine the vertices of a triangle, show that `(1)/(2)[vecbxxvecc+veccxxveca+vecaxxvecb]` givens the vector area of the triangle. Hence, deduce the condition that the three points `veca,vecband vecc` are collinera. Also, find the unit vector normal to the plane of the triangle.

Answer

Unit vector to the plane `triangleABC = (veca xx vecb + vecb xx vecc + vecc xx veca)/(|veca xx vecb + vecb xx vecc + vecc xx veca|)`