I have created a 1 sq.ft face along the XY plane using the eye of a camera as its centroid:

```
model = Sketchup.active_model
entities = model.active_entities
view = model.active_view
cam = view.camera
eye = cam.eye
target = cam.target
pts = [
Geom::Point3d.new(eye[0] - 0.5.feet, eye[1] - 0.5.feet, eye[2]),
Geom::Point3d.new(eye[0] + 0.5.feet, eye[1] - 0.5.feet, eye[2]),
Geom::Point3d.new(eye[0] + 0.5.feet, eye[1] + 0.5.feet, eye[2]),
Geom::Point3d.new(eye[0] - 0.5.feet, eye[1] + 0.5.feet, eye[2])
]
gr = entities.add_group
square = gr.entities.add_face ( pts )
```

I want the square to be perpendicular to the eye-target vector, i.e., rotating the square so the eye-target vector is a normal to its plane. I’ve tried the following geometry equations with no success:

```
n = [0, 0, 1] # Current normal vector to the square
v = [target[0] - eye[0], target[1] - eye[1], target[2] - eye[2]] # eye-target vector
axis = [v[1], -v[0], 0] # Axis of rotation given by vectorial product (v x n)
magnitude = Math.sqrt( axis[0]**2 + axis[1]**2 + axis[2]**2 ) # Magnitude of axis
u = [axis[0]/magnitude , axis[1]/magnitude , axis[2]/magnitude ] # Normalized axis
theta = -Math.acos( v[2] / Math.sqrt(v[0]**2 + v[1]**2 + v[2]**2) ) # Angle of rotation given by scalar product (v · n)
```

The current normal vector to the square is n = [0,0,1] since it is generated along the XY plane. To calculate the new axis of rotation, a vectorial product (v x n) is needed, and then the axis is normalized. In the same way, I calculate the angle of rotation theta by the scalar product (v · n).

Having the point, the axis, and the angle, I can set the transformation:

```
tr = Geom::Transformation.rotation( eye, u, theta )
gr.transform!(tr)
```

But the result is not the expected. Could you help me to localize my mistake? Any other idea to solve the issue will be very welcomed too.