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If u=ax+by+cz, v=ay+bz+cx, w=ax+bx+cy, t...

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

A

`u^(2)+v^(2)+w^(2)-2uvw`

B

`u^(3)+v^(3)+w^(3)-3uvw`

C

`0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(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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