Question

(1 point) Find the volume of the parallelepiped with one vertex at (4,2,4), and adjacent vertices at (6,3,8), (6,1,10), and (0,6,3)

Answer 1

8 cubic units

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]|

=
`$ \begin{vmatrix}\ 2\ \ \ 1\ \ \ \ 4\ \\2\ -1\ \ \ 6 \\-4\ \ \ 4\ -1 \end{vmatrix}$`

= |2(1-24)+1(-2+24)+4(8-4)|

= |2(-23) + 1(22) + 4(4)|

= |8|

=8 cubic units