Here is the task that I need to solve:
"Let a,b,c are non-coplanar vectors and p,q,r are three vectors. Show that p,q,r are non-coplanar if and only if there exist numbers where "
I know that I need to show it in both ways that is:
If p,q,r are non-coplanar then there exist numbers where
and
If exist numbers where then p,q,r are non-coplanar.
I will begin with the second case.
I need to show that u*p+v*q+w*r=0 leads to u=v=w=0.
I know the fact that m*a+n*b+l*c=0 leads to m=n=l=0
So that +
and
+
Only I do not know if its valid to take:
In this case because of m=n=l=0 then u=v=r=0.
Please help.