Need help for vector product

[sourav das]

I really need some help about vector product. (Specially cross multiplication) And i want an answer with explanation of the value of \[\vec{a}\times \vec{b}= ?\] where \[\vec{a}= \frac{2\vec{x}+\vec{y}}{3}\]
And \[\vec{b}= \frac{2\vec{p}+\vec{q}}{3}\]

[Moon]

Physically the cross product means the area of a parallelogram with two adjacent sides $\vec{a},\vec{b}$.
$\dfrac{2\vec{x}+\vec{y}}{3}$ means the position vector of a point which has $\vec{x}$ and $\vec{y}$ as the position vector of the terminal points (and the segment between those two terminal points is divided into ratio $2:1$ by the first point).

I don't think that we can specifically conclude anything special from just these equations. We need more info about what we want to prove.

[Mehfuj Zahir]

In 3 d space to calculate the vector product you must know about three axis .Here you dont mentioned about axis and its not possible to give answer according to given condition

[tanvirab]

from the information you have given, the only thing that can be found is:

$\vec{a}\times \vec{b}= \frac{4}{9} \vec{x} \times \vec{p} + \frac{2}{9} \vec{x} \times \vec{q} + \frac{2}{9} \vec{y} \times \vec{p} + \frac{1}{9} \vec{y} \times \vec{q}$

[sourav das]

Oh! I forget to mention, it is 2d space. (Actually i got it when i was solving a Geometry Unbound problem)