I try to calculate the rotation matrix that needs to applied on one reference frame to match a second reference frame. I have the following code:

```
# test calculation of the orientation
using LinearAlgebra, Rotations, StaticArrays, Test
"""
rot3d(ax, ay, az, bx, by, bz)
Calculate the rotation matrix that needs to be applied on the reference frame (ax, ay, az) to match
the reference frame (bx, by, bz).
All parameters must be 3-element vectors. Both refrence frames must be orthogonal,
all vectors must already be normalized.
Source: [TRIAD_Algorithm](http://en.wikipedia.org/wiki/User:Snietfeld/TRIAD_Algorithm)
"""
function rot3d(ax, ay, az, bx, by, bz)
R_ai = hcat(ax, az, ay)
R_bi = hcat(bx, bz, by)
return R_bi * R_ai'
end
ax = [1, 0, 0]
ay = [0, 1, 0]
az = [0, 0, 1]
x = [1, 0, 0]
y = [0, 1, 0]
z = [0, 0, 1]
rot1 = rot3d(ax, ay, az, x, y, z)
q1 = QuatRotation(rot1)
@test all(Rotations.params(q) .== SVector{4, Float64}([1.0 0 0 0]))
x = [-1, 0, 0]
y = [0, 1, 0]
z = [0, 0, 1]
rot2 = rot3d(ax, ay, az, x, y, z)
q2 = QuatRotation(rot2)
```

If I look at the result:

```
julia> q1
3Γ3 QuatRotation{Float64} with indices SOneTo(3)ΓSOneTo(3)(QuaternionF64(1.0, 0.0, 0.0, 0.0)):
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
julia> q2
3Γ3 QuatRotation{Float64} with indices SOneTo(3)ΓSOneTo(3)(QuaternionF64(1.0, 0.0, 0.0, 0.0)):
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
```

both rotations are the same, which cannot be correct. So there must be a mistake in my function `rot3d`

.

How can I implement it correctly?