The three vectors A, B, and C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by 1/2|(BxC)+(CxA)+(AxB)|.
The Attempt at a Solution
I know that the magnitude of the cross product of any two vectors gives the area of the parallelogram formed by those two vectors, and taking half of that would give the area of the triangle. I can see how 1/2|BxC|+1/2|CxA|+1/2|AxB| could give the total area of the triangle formed by the three points, because that would give the sum of the areas of the triangles formed by all 3 possible pairs of vectors which would equal the area of the triangle formed by all 3 vectors. I don't believe that this is the same thing as 1/2|(BxC)+(CxA)+(AxB)|. Not sure where to go from here.