On the coordinate calculation of vector If vectors a (3cos α, 3sin α, 1), B (2cos θ, 2Sin θ, 1), then the value range of | A-B | is?

On the coordinate calculation of vector If vectors a (3cos α, 3sin α, 1), B (2cos θ, 2Sin θ, 1), then the value range of | A-B | is?

Since the Z coordinates are equal, the problem of plane is not considered
Consider the geometric meaning of the coordinate 3cos α, you will find that the end point of a is on the circle with (0,0,1) as the center and 3 as the radius, and the end point of B is on the concentric circle with 2 as the radius. Then the maximum modulus of the difference between the two vectors is 5 and the minimum is 1. That is to take the farthest and nearest points on the two circles and calculate the length of the line