Question

Find the volume of a parallelopiped whose coterimus edges are represented by the vectors `hat"i" + hat"k", hat"i" + hat"k", hat"i" + hat"j"`. Also find volume of tetrahedron having these coterminus edges.

Answer 1

Let `bar"a" = hat"j" + hat"k", bar"b" = hat"i" + hat"k" and bar"c" = hat"i" + hat"j"` be the coterminus edges of a parallelopiped.

Then volume of the parallelopiped = `[bar"a"  bar"b"  bar"c"]`

`= |(0,1,1),(1,0,1),(1,1,0)|`

= 0(0 - 1)- 1(0 - 1) + 1(1 - 0)

= 0 + 1 + 1 = 2 cu units

Also, volume of tetrahedron = `1/6 [bar"a"  bar"b"  bar"c"]`

`= 1/6(2) = 1/3` cubic units