# If  u , v ,w are non-coplanar vectors and p,q are real numbers, then the equality

If $$\overrightarrow{\mathrm{u}}, \overrightarrow{\mathrm{v}}, \overrightarrow{\mathrm{w}}$$ are non-coplanar vectors and $$\mathrm{p}, \mathrm{q}$$ are real numbers, then the equality $$[3 \vec{u} p \vec{v} p \vec{w}]-[p \vec{v} \vec{w} q \vec{u}]-[2 \vec{w} q \vec{v} q \vec{u}]=0$$ holds for :-

• (1) More than two but not all values of (p,q)
• (2) All values of (p, q)
• (3) Exactly one value of (p, q)
• (4) Exactly two values of (p, q)
from [AIEEE-2009]