Find a vector which is orthogonal to P=(1,2,3) with respect to Q=(0,-2,-3) and normalize that vector.
Then please answer the question. What does "$\displaystyle \vec{u}$ orthogonal to $\displaystyle \vec{v}$ with respect to $\displaystyle \vec{w}$" mean? I know what it means for two vectors to be "orthogonal" but not "with respect to" a third vector. Could you possibly mean "orthogonal to both $\displaystyle \vec{u}$ and $\displaystyle \vec{v}$"? Or are you asking about the "Orthogonal projection of $\displaystyle \vec{v}$ on $\displaystyle \vec{w}$?