Check a point by substituting into a plane

Write the plane as $\mathbf r\cdot(3,-3,2)=3$. Substitute the position vector of Q into the left-hand side:

$\begin{aligned}(1,2,3)\cdot(3,-3,2)&=3-6+6\\&=3.\end{aligned}$

This equals the right-hand side, so Q satisfies the plane equation and lies on it. This is the complete substitution proof from the Teacher copy; the Student working space is blank.