Draw a circle with a unit length of 1, that is, take the modulus of vector b as the radius. Draw a ray from the center of the circle. Finding a point on this ray leads to an angle of 60 degrees with the center of the circle and tangent to the circle. The distance from the center of the circle to this point is the maximum. The range of a is 0 to this value. You can find one.

Max=2 times the root number 3.

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The reason is explained as follows. First of all, vector b-a is a vector from the endpoint of A to the endpoint of B, and its angle with A is 120 degrees, so the angle of A is 60 degrees (that is, these two vectors are 120 degrees).

Therefore, all rays at an angle of 60 degrees from the straight line drawn from the origin can be picked up. Excluding the center of the circle (A in the title is not equal to 0).

So the outermost one can reach the one tangent to the garden, and the rest can't. So the range of a is (0,2 times the root number 3.

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