Problem involving cross products

Question

I have a problem in vector algebra. In this Wolfram-page the last two formulas (9) and (10) are: $$ \frac{ | (x_2 - x_1) \times (x_1 - x_0) | }{|x_2 - x_1 |} = \frac{ | (x_0 - x_1) \times (x_0 - x_2) | }{|x_2 - x_1 |} $$ I've tried to apply properties founded in this other Wolfram-crossproduct-page but I still don't understand it. How is possible? And why the do this vectors manipulation?

Answer 1

$\begin{align}|(x_2-x_1)\times(x_1-x_0)|&=|(x_1-x_2)\times(x_0-x_1)|\\&=|(x_0-x_1)\times(x_1-x_2)|\\&=|(x_0-x_1)\times((x_0-x_1)+(x_1-x_2))|\\&=|(x_0-x_1)\times(x_0-x_2)|\end{align}$

where the second is because you are in magnitude signs and the third is because the cross product of a vector with itself (or any parallel vector) is zero.