Answer to Question #2881 in Linear Algebra for anne

Question

Let a,b and c be three vectors such that a + b + c = 0. Given that a x b = b x c = c x a. Explain what this means geometrically. (Your answer should refer to a triangle)

Answer 1

If a+b+c = 0, he vectors a,b,c lay on the same plane and we can construct the triangle using these vectors.
a x b = b x c = c x a& - you can make sure that if the vectors form the triangle, the pairwise products of them would be equal, since the vector product equals the the area of the parallelogram with vectors as sides, which, in turn, equals to double area of the triangle.