Calculate the volume of a Parallelepiped given the vectors f

Calculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex. A = a_x, B = a_y, C = a, D = 2a_x E = 2a_y, F = a_x + a_y

Solution

Ans)

a) Volume of a parallelepiped=A.(BxC)=a_x.(a_yxa_z)=a_x.a_x=1

b) Volume of a parallelepiped=D.(ExF)=2a_x.(2a_yx (a_x+a_y))=2a_x.( 2a_y x a_x + 2a_y x a_y)=2a_x.( 2-a_z  +0)=0