# Thread: Vector space

1. ## Vector space

Find a vector which is orthogonal to P=(1,2,3) with respect to Q=(0,-2,-3) and normalize that vector.

2. What do you mean with "with respect to"? Are you searching vector orthogonal to $\displaystyle \vec{PQ}$?

3. No

4. 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 $\displaystyle \vec{w}$?

5. Originally Posted by roshanhero
P=(1,2,3)
Q=(0,-2,-3)
is standard notation for coordinates of points. So what yu have posted is qute ambiguous. Are we meant to assume that P is a vector given by <1, 2, 3> and Q is a vector given by <0, -2, -3>?

Also, I support the several requests for clarification of the question.