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

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) (Show Source): You can put this solution on YOUR website!
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The volume of the given parallelepiped is equal to the absolute value of the determinant of the 3x3-matrix


    Volume = | det  |.


So, calculate the determinant first


    det  = 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

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