I do not have Illustrator, but need to send a file to someone as a vector. Can I save my Photoshop image as a vector?
If you used vector elements in Photoshop (like shapes, smart objects, fonts etc.), you can save as eps. Then, send the eps to that someone. He/she can open the eps in Illustrator and enjoy the vectors.
You may also use Pixel2Vector - free plugin for Photoshop
What it does?
It converts directly a raster image/shape into vector format. In Photoshop.
Where goes the new vector?
Above the original layer.
How good it is?
Not as good as image tracing in Illustrator; depends heavily on the image (the bigger in size, the more accurate the tracing).