1.

If u=ax+by+cz, v=ay+bz+cx, w=ax+bx+cy, then the value of |{:(a,b,c),(b,c,a),(c,a,b):}|xx|{:(x,y,z),(y,z,x),(z,x,y):}| is

Answer»

`U^(2)+v^(2)+w^(2)-2uvw`
`u^(3)+v^(3)+w^(3)-3uvw`
`0`
none of these

Solution :`(B)` `Delta_(1)Delta_(2)=|{:(ax+by+cz,ay+bz+cx,az+bx+cy),(bx=cy+az,by+cz+ax,bz+cx+ay),(cx+ay+bz,cy+az+bx,cz+ax+by):}|`
`=|{:(u,v,w),(w,u,v),(v,w,u):}|`
`=u(u^(2)-vw)-v(wu-v^(2))+w(w^(2)-uv)`
`=u^(3)+v^(3)+w^(3)-3uvw`


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