I am making a 3d isometric game in which I have a sprite emitting two rays in perpendicular directions (on the x and z axis). Does anyone know how I could make it so that if the mouse cursor is positioned between the two rays, the sprites frame will change. I have no code so far as I have absolutely no clue where to start.

If you have two rays you basically have two straight lines, if they are perpendicular you have two Directions and therefor two vectors

Vector3.forward is your Z and Vector3.right is your X

forward = (0,0,1);
right = (1,0,0);

regardless of where you mouse is the direction from the origin of these rays to the point of your mouse will be between (1,0,0) and (0,0,1)

if your mouse in perfectly between both your normalized vector will be (1,0,1)

All of this combined means :

Cast a ray from your camera to the mouse position, get the 3d vector of the hit, get the direction of the hit from the origin of the two initial rays, if the direction meets criteria, change sprite frame

Ray ray = Camera.main.ScreenPointToRay(Input.touch.position);
RaycastHit hit;
if(Physics.Raycast(ray, out hit, 100))
{
directionVector = hit.position - originOfRays
Vector3.Normalize(directionVector);
if(directionVector.x >= 0 && directionVector.z >= 0)
{
//change frame
}
}

I would start by using Unity’s mathematical Plane class to create a plane at the same position as your sprite and parallel the XZ plane. You can then use Plane.Raycast() to find the point on the plane for your test. I’m fuzzy about the actual test, but lets assume that you are casting your rays at Vector3.forward and Vector3.right. If so, a simple way to make the determination is to convert the point into local space. If the point has a positive ‘z’ and positive ‘z’ value, then it will be between the two rays.

#pragma strict
function Update() {
Debug.DrawRay(transform.position, Vector3.forward * 20.0);
Debug.DrawRay(transform.position, Vector3.right * 20.0);
var plane = new Plane(Vector3.up, transform.position);
var ray = Camera.main.ScreenPointToRay(Input.mousePosition);
var enter : float;
if (plane.Raycast(ray, enter)) {
var hitPoint = ray.GetPoint(enter);
hitPoint = transform.InverseTransformPoint(hitPoint);
if (hitPoint.x > 0.0 && hitPoint.z > 0.0) {
Debug.Log("In the zone");
}
}
}

If you two rays have a different definition, then the ‘between’ test will need to change, but the rest of the code would remain the same.