Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(3,0,1), Q(-1,2,5), R(5,1,-1) and S(0,4,2).

Question

Ben Owens · Accepted Answer

As we have three vectors, there is a product, called scalar triple product, that gives the volume of the parallelepiped that has the three vectors as dimensions.    PQ→=(3+1,0−2,1−5)=(4,−2,−4)    PR→=(3−5,0−1,1+1)=(−2,−1,2)    PS→=(3−0,0−4,1−2)=(3,−4,−1)    The derminant is given for example with the Laplace rule:    4×[(−1)(−1)−(2)(−4)]−(−2)[(−2)(−1)−(2)×(3)+(−4)[(−2)(−4)−(−1)(3)]=4(1+8)+2(2−6)−4(8+3)=36−8−444=−16    Thus, V=16

rodclassique4r · Accepted Answer

PQ=(3+1,0−2,1−5)=(4,−2,−4)  PR=(3−5,0−1,1+1)=(−2,−1,2)  PS=(3−0,0−4,1−2)=(3,−4,−1)  Thus, V=16 is the volume

Find the volume of the parallelepiped with adjacent edges PQ,

Answered question

Answer & Explanation

New Questions in Integral Calculus