How to create 2 vectors parallel to a plane? or Parallel to Hit.point? For hand IK placement

I'm want to make a script that scans an obstacle and then creates two vectors for the IK Hand position, so when the player gets close to the object they can climb over it or vault over it. I made a SphereCast that returns a normal and a point.

First I made this: hit.point + -transform.right _leftHandOffset hit.point + transform.right _rightHandOffset

But then realized that the two vectors will not be parallel to the object. Instead, I tried to take the hit.point subtract it from the normal and multiply it with the dot product of these two vectors. Just wished for the best... But I'm bad at Math.

 hit.point - normal * Vector3.dot(hit.point, normal);

Is there a way to create a vector that is parallel to the plane of this object or maybe another solution?

Any help will be much appreciated.