Question

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(1, 0, −1), Q(3, 3, 0), R(3, −3, 0), S(1, −2, 2)

Answer 1

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] = $\begin{bmatrix}2 & 3 &1 \\ 2 & -3 &1 \\ 0 & -2 &3 \end{bmatrix}$

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