AIEEE 2009 (Offline)Question 1
If $\vec u,\vec v,\vec w$ are non-coplanar vectors and $p,q$ are real numbers, then the equality $\left[3\vec u\ \ p\vec v\ \ p\vec w\right]-\left[p\vec v\ \ \vec w\ \ q\vec u\right]-\left[2\vec w\ \ q\vec v\ \ q\vec u\right]=0$ holds for :
Vector Algebra
Solution
The left side is $(3p^2-pq+2q^2)[\vec u\ \vec v\ \vec w]$. $3p^2-pq+2q^2=0$ has discriminant $-23q^2$ in $p$, so only $p=q=0$: exactly one value.