`1.` If `vec(a),vec(b),vec(c) ` are position vectors of vertices `A,B` and `C` with respect to `O`, then volume of tetrahedron `OABC` represented by `V` is given by
`quadquadquadquadquadV =1/3 ` Base area `xx` height

Base Area `=1/2 |vec(a) xx vec(b) + vec(b) xx vec(c) +vec(c) xx vec(a) |`

Let `vec(a) xx vec(b) +vec(b) xx vec(c) +vec(c) xx vec(a) =vec(n)`

`quadquadquadquadquad:.` Base area `=1/2 |vec(n) |`

Height `=` projection of `vec(a) ` on `vec(n)`

`quadquadquadquad= |vec(a)*vec(n) | / |vec(n) | = |vec(a)* ( vec(a) xx vec(b) +vec(b) xx vec(c)+vec(c) xx vec(a) ) | /|vec(n) | = | [vec(a)vec(b)vec(c) ] |/|vec(n) |`

`:.` `quadquadquadquadV= 1/3 *1/2 | vec(n)| |[vec(a)vec(b)vec(c) ] |/|vec(n) | =1/6 |[vec(a)vec(b)vec(c) ] |`

`2.` If `vec(a),vec(b),vec(c),vec(d)` are position vectors of vertices `A,B,C,D` of a tetrahedron `ABCD` then

its volume = ` {tt( (1/6 | [ (vec(AB) , vec(AC) , vec(AD)) ] |) , (text (or)) , ( 1/6 | [ (vec(b)-vec(a) , vec(c)-vec(a) , vec(d)-vec(a)) ] |) )`