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 ]|
= 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 .
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