Question

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

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

Answer 1

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"`