SOLUTION: Find the volume of the parallelepiped determined by the vectors →a=⟨5,3,−1⟩, →b=⟨0,4,2⟩, →c=⟨2,5,1⟩.

Algebra ->  Vectors -> SOLUTION: Find the volume of the parallelepiped determined by the vectors →a=⟨5,3,−1⟩, →b=⟨0,4,2⟩, →c=⟨2,5,1⟩.      Log On


   

Question 1141441: Find the volume of the parallelepiped determined by the vectors →a=⟨5,3,−1⟩, →b=⟨0,4,2⟩, →c=⟨2,5,1⟩.
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
The volume of the given parallelepiped is equal to the absolute value of the determinant of the 3x3-matrix


    Volume = | det %28matrix%283%2C3%2C++5%2C+3%2C+-1%2C++0%2C+4%2C+2%2C++2%2C+5%2C+1%29%29 |.


So, calculate the determinant first


    det %28matrix%283%2C3%2C++5%2C+3%2C+-1%2C++0%2C+4%2C+2%2C++2%2C+5%2C+1%29%29 = 5*(4*1 - 5*2) - 3*(0*1 - 2*2) + (-1)*(0*5 - 2*4) = -10,


and then take its absolute value as the volume


    Volume = | -10 | = 10.      ANSWER