The nonzero vectors a and B satisfy: | B | = 1, and the angle between B and B-A is 30 degrees. Please give us a detailed explanation

The nonzero vectors a and B satisfy: | B | = 1, and the angle between B and B-A is 30 degrees. Please give us a detailed explanation

|A |, | B |, | B-A | form a triangle, | B | = 1 fixed length, and the angle between | B |, | B-A | is 30 degrees. The starting points of a vector and B vector coincide. When a vector is perpendicular to B-A vector, | a | min = 1 / 2, and | a | Max is unlimited
So, the maximum range of | a | is [1 / 2, + infinity]