Let \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) be three vectors that lie on the same line. Find \(\mathbf{a} \times \mathbf{b} + \mathbf{b} \times \mathbf{c} + \mathbf{c} \times \mathbf{a}\)
The cross product of any two vectors that lie on the same line is zero. Hence a x b + b x c + c x a is a zero vector.
