A rectangle pyramid is sliced parallel to its base as shown in the figure. What is the shape of the resulting two-dimensional cr
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Answer:
the volume of the parallelepiped is = 36
Step-by-step explanation:
given,
P(1, 0, −1), Q(3, 3, 0), R(3, −3, 0), S(1, −2, 2)
PQ = Q - P = (2, 3, 1)
PR = R - P = (2, -3 , 1)
PS = S - P = (0, -2 , 3)
now volume of parallelopiped
[PQ PR PS] =
now calculating determinant of the matrix
= 2 (-9+2) - 3 (6-0) + 1 (-4-0)
= -14 - 18 - 4
= -36
hence , the volume of the parallelepiped is = 36