# $A(2,1,3),B(3,2,4),C(1,8,9), D(4,3,12).$ Find the volume of a parallelepiped with vectors $\vec{AB}$, $\vec{AC}$, $\vec{AD}$.

$A(2,1,3)$

$B(3,2,4)$

$C(1,8,9)$

$D(4,3,12)$

Find the volume of a parallelepiped with vectors $\vec{AB}$, $\vec{AC}$, $\vec{AD}$. I am not sure how to calculate this. How do I calculate the distance between $A$ and $B$?

Is the distance of $\vec{AB}$ calculated this way $|\vec{AB}| = \sqrt{5^2+3^2+7^2} = \sqrt{83}$?

So I can then get the distance of $\vec{AB}$, $\vec{AC}$, $\vec{AD}$ this way and then go from there? I've forgotten all about vectors and this exercise has been troubling me for some time now and I'm not sure if I'm doing this the correct way. What's the simplest way of getting this one done?

• The volume is simply $(\overrightarrow{AB} \times \overrightarrow{AC}) \cdot \overrightarrow{AD}$ Dec 29 '14 at 3:46