How do I make a BodyVelocity that moves perpendicularly to the pointer?

I've been able to use HumanoidRootPart.BodyVelocity.Velocity = mouse.Hit.lookVector*16 to move the player forwards/backwards relative to the pointer, but I'm not sure how to strafe sideways depending on where the mouse is pointed.

Perhaps even have a better way to move a floating character mid-air, while staying on the same Y (vertical) level? (as that's what I was trying to achieve with this)