Question

Determine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at (0, 1, 0), (4, 1, -3), and (4, -3, -2). Volume = 0

Answer 1

Solution-

Since one vertex of parallelepiped is at origin and other the other 3 vertices are (0,1,0), (4, 1, -3), (4, -3, -2).

So, we can say that that three vectors representing the edge of parallelepiped are

a = 0i + 1j + 0k

b = 4i + 1j -3k

c = 4i -3j -2k

Now, The volume of parallelepiped is given by the magnitude of scaler triple product

=|[a b c ]|

$=\begin{vmatrix} 0 & 1& 0\\ 4& 1 & -3\\ 4& -3 & -2 \end{vmatrix}$

= 0[(1×-2) - (-3×-3)] -1[(4×-2) -(4×-3)] +0[(4×-3) -(4×1)]

= 0 - 1[(-8) -(-12)] + 0

= -[-8 +12]

= -[-4]

= 4

Hence, the volume of parallelepiped is 4 .