I want to calculate the volume of the tetrahedron defined by those 4 points:
$$ P_1 = (-0.0865403, -0.122347, 0.898904)\\ P_2 = (-0.436523, -0.30131, 1.92251)\\ P_3 = (-0.459102, -0.0670386, 1.68168)\\ P_4 = (0,0,0) $$
How would you calculate this volume?
I'm doing
$$B_1 = P_1-P_4 = P_1\\B_2 = P_2-P_4 = P_2\\B_3 = P_3-P_4 = P_3$$
which is an equation that I found (is it correct?)
then
$$V = \frac{|B_1\cdot(B_2\times B_3)|}{6} = \frac{|(-0.0865403, -0.122347, 0.898904)\cdot((-0.436523, -0.30131, 1.92251)\times (-0.459102, -0.0670386, 1.68168))|}{6}$$
Which is 0.00786195 according to wolfram alpha (see here and divide by 6).
I have 2 questions: am I calculating the tetrahedron volume correctly? Does the order of points matter in the equation?