# Math Help - Vector to rotation

1. ## Vector to rotation

Hi,

I have this small problem. I have looked on the internet and I found some answers but they weren't 100% clear.
Let's say I have two 3D vectors:

x: -0.551020951227745 y: 0.291595823345109 z: 0.781887323797847
and
x: -0.881938222372968 y: -0.362656707254797 z: 0.301106434007507

I need to find the rotation matrix which rotates the first vector onto the second one. Can somebody explain to me how I do this exactly? Like with a formula or something? Thx

2. Never mind, problem solved, if anyone else ever needs it, here's the solution in matlab code, im assuming it's readable even if u can't read matlab code, cross = cross product and dot = dot product:

Code:
    u = normal_vectors(1);
v = normal_vectors(2);
n = cross(u,v);
n = n/norm(n);
phi = acos(dot(u,v) / (norm(u) * norm(v))); %in radials

t = (1-cos(phi));
s = sin(phi);
d = cos(phi);

a = n(1);
b = n(2);
c = n(3);

Rmatrix = [   t*a^2+d t*a*b-s*c t*a*c + s*b;
t*a*b + s*c t*b^2+d t*b*c - a*s;
t*a*c - s*b t*b*c+s*a t*c^2 + d
];
So you end up with a rotation matrix which if applied rotates like the first vector to the second