Find the volume of the parallelepiped with adjacent edges PQ,

killjoy1990xb9 2021-12-16 Answered
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).
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Ben Owens
Answered 2021-12-17 Author has 27 answers
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+1,02,15)=(4,2,4)
PR=(35,01,1+1)=(2,1,2)
PS=(30,04,12)=(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(26)4(8+3)=368444=16
Thus, V=16

We have step-by-step solutions for your answer!

rodclassique4r
Answered 2021-12-18 Author has 37 answers
PQ=(3+1,02,15)=(4,2,4)
PR=(35,01,1+1)=(2,1,2)
PS=(30,04,12)=(3,4,1)
Thus, V=16 is the volume

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions