How can a vector be perpendicular to two non parallel vectors?

I have a homework question which asks you to find a vector that is perpendicular to two vectors which are not parallel, how can that happen?|||This sometimes gets tricky in three dimensions. Hold a pencil in front of you with the point facing you. Now hold another pencil directly above that with the point facing directly to the right. Both pencils should now be horizontal to the floor yet not parallel to each other! Then a third pencil could be held vertically (perpendicular to the floor) with the point facing straight up and go perpendicular to both pencils because the two pencils are horizontal with the floor but the third pencil is vertical (perpendicular) to the floor. Hope that helps.|||This is so in 3-space, but not the plane.





Any two linearly indep vectors in 3-space determine a plane and a perpendicular to such a plane will be perp to any vector in the plane.|||At any point along its length, in three dimensions, a vector is perpendicular to a plane and any and all vectors on that plane.