Question

Find the volume of the parallelopiped whose coterminous edges are `2hati - 3hatj, hati + hatj - hatk` and `3hati - hatk`.

Answer 1

Let `bara = 2hati - 3hatj`,

`barb = hati + hatj - hatk`,

`barc = 3hati - hatk`

Volume of parallelopiped

= `[(bara, barb, barc)]`

= `|(2, -3, 0),(1, 1, -1),(3, 0, -1)|`

= 2(–1 – 0) + 3(–1 + 3)

= –2 + 6

= 4 cub. units