Answer:
8 cubic units
Step-by-step explanation:
Let he vertices of the parallelepiped be A = (4,2,4), B= (6,3,8), C = (6,1,10) and D = (0,6,3)
The edges of the parallelepiped are
AB = (6,3,8) - (4,2,4) = (2,1,4)
AC = (6,1,10) - (4,2,4) = (2,-1,6)
AD = (0,6,3) - (4,2,4) = (-4,4,-1)
Therefore the volume of the parallelopiped is = |[AB,AC,AD]|
= [tex]$ \begin{vmatrix}\ 2\ \ \ 1\ \ \ \ 4\ \\2\ -1\ \ \ 6 \\-4\ \ \ 4\ -1 \end{vmatrix}$[/tex]
= |2(1-24)+1(-2+24)+4(8-4)|
= |2(-23) + 1(22) + 4(4)|
= |8|
=8 cubic units
