It is known that the included angle of non-zero vectors a and B is 60 ° and | a | = | B | = 2. If vector C satisfies (A-C); (B-C) = 0, then | C | = 2? Is to find the value range

It is known that the included angle of non-zero vectors a and B is 60 ° and | a | = | B | = 2. If vector C satisfies (A-C); (B-C) = 0, then | C | = 2? Is to find the value range

Establish the coordinate system, take the straight line of the bisector of a and B as the x-axis,
Let a coordinate be (√ 3,1), B coordinate be (√ 3, - 1),
(the establishment of coordinate system is not unique, but the calculation is relatively simple.)
Let the coordinates of C be (x, y),
Then we know that (√ 3-x, 1-y) (√ 3-x, - 1-y) = 0,
There are: (x - √ 3) ^ 2 + y ^ 2 = 1
This is a circle
The maximum value of | C | is required, that is, to find a point on the circle which is farthest from the origin. Obviously (1 + √ 3,0) should be taken. At this time, there is a maximum value of 1 + √ 3
The minimum value of | C | is required, that is, to find a point on the circle closest to the origin. Obviously (√ 3-1,0) should be taken. At this time, there is a maximum value √ 3-1
Therefore, the value range of | C | is [√ 3-1, √ 3 + 1]