% define symbolic terms
x = sym('x','real');
y = sym('y','real');
z = sym('z','real');
n1 = sym('n1','real');
n2 = sym('n2','real');
n3 = sym('n3','real');
a = sym('a','real');
b = sym('b','real');
c = sym('c','real');

% assumption
assume(n1^2+n2^2+n3^2==1);

% define terms
sintheta=(n3)/(n1^2+n2^2+n3^2)^(0.5);
costheta=(n1^2+n2^2)^(0.5)/(n1^2+n2^2+n3^2)^(0.5);
u=[-n2;n1;0];
uX=[0,0,n1;0,0,n2;-n1,-n2,0];

% create rotation matrix
Q=costheta*eye(3)+sintheta*uX+(1-costheta)*u*u.';
Q=simplify(Q)