It is known that vectors a and B are basic units, and vector a is multiplied by vector b = 0. If vector C satisfies | C-A-B | = 1, then the value range of | C | is

It is known that vectors a and B are basic units, and vector a is multiplied by vector b = 0. If vector C satisfies | C-A-B | = 1, then the value range of | C | is

It is known that | a | = | B | = 1, and a * b = 0,
Then from (a + b) ^ 2 = a ^ 2 + B ^ 2 + 2A * b = 2, we get | a + B | = √ 2
Because | C-A-B | = 1,
So 1 = | C - (a + b) | = | (a + b) - C | & gt; = | a + B | - | C |, we get | C | & gt; = √ 2-1,
At the same time, 1 = | C - (a + b) | & gt; = | C | - | a + B |, we get | C | & lt; = √ 2 + 1,
So the value range of | C | is [√ 2-1, √ 2 + 1]