Question

Find the volume of the parallelopiped whose coterminus edges are given by vectors `2hati+5hatj-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+5hatj-4hatk`

`vecb= 5hati+7hatj+5hatk`

`vecc=4hati+5hatj-2hatk`

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

`=2(-14-25)-5(-10-20)-4(25-28)`

`=2(-39)-5(-30)-4(-3)`

`=-78+150+12`

`=84 cube" "Unit`