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### Question Asked by a Student from EXXAMM.com Team

** Q 2221412321. ** Let `vec(a) , vec(b)` and `vec(c)` be three non-zero and non-coplanar vectors

and `vec(p) ,vec(q)` and `vec(r)` be three vectors given by

`vec(p) = vec(a) + vec(b) -2 vec(c) , vec(q) = 3 vec(a) - 2vec(b) + vec(c)` and

`vec(r) = vec(a) -4 vec(b) +2vec(c)`

the volume of the parallelopiped determined by `vec(a) ,vec(b)`

and `vec(c)` is `V_1` and that of the parallelopiped determined by

`vec(p) , vec(q)` and `vec(r)` is `V_2` then `V_2 : V_1` is equal to