Question

Find the volume of a parallelopiped whose edges are represented by the vectors:

`vec a = 2 hat i - 3 hat j - 4 hat k`, `vec b  = hat i + 2 hat j - hat k` and `vec c = 3 hat i +  hat j +  2 hatk`

Answer 1

Volume of parallelopiped = `[vec avec b vec c]`

`= |(2,-3,-4),(1,2,-1),(3,1,2)|`

`= 2(4+1) + 3(2 + 3) - 4(1 - 6)`

= 10 + 15 + 20

= 45 cubic units