Determine the volume of the parallelepiped with one vertex a

Determine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at (0, 1, 0), (2, -2, 2), and (2, -3, 3). Volume = 0

Solution

origin (0, 0 , 0) is the inital point, so the three vectors

a, b, c are :

a = (0,1,0) , b =( 2, -2,2) and c = ( 2, -3 ,3)

So, Volume of parallelepiped is the is the magnitude of their scalar triple product:

= |a.(bxc)|

vector product bxc =( 2, -2,2)  x ( 2, -3 ,3) = (0 , -2, -2)

Volume = |a.(bxc)| =| (0, 1, 0).(0, -2,-2) | = |0- 2| = 2

Volume = 2 units