I know that if
$ F(x,y,z)=0 $
is a surface, then the angle of inclination at the point $(x_0, y_0, z_0)$ is defined by the angle of inclination of the tangent plane at the point or
$\cos(A)=\dfrac{\nabla F(x_0,y_0,z_0)*k}{|\nabla F(x_0,y_0,z_0)|}$
my question is just what is a k? Is it about i,j,k? Which are just component of vectors? or for example what is equal to following $<1/2,1/2,1/2>*k$? and why? thanks