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# Find the volume of the parallelopiped whose coterminus edges are given by vectors 2i+3j-4k, 5i+7j+5k and 4i+5j-2k - Mathematics and Statistics

#### Question

Find the volume of the parallelopiped whose coterminus edges are given by vectors

2hati+3hatj-4hatk, 5hati+7hatj+5hatk and 4hati+5hatj-2hatk

#### Solution

If veca vecb and vec c are conterminus edges of parallelopiped then the volume of the parallelopiped =[ veca  vecb   vecc ]

where veca=2hati+3hatj-4hatk

vecb= 5hati+7hatj+5hatk

vecc=4hati+5hatj-2hatk

therefore V=[veca vecb vecc]=[[2,3,-4],[5,7,5],[4,5,-2]]

=2(-14-25)-3(-10-20)-4(25-28)

=2(-39)-3(-30)-4(-3)

=-78+90+12

=24 "cube  Unit"

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