Question

Two unit vectors is also unit vector then magnitude of the differences

Answer 1

the magnitude of their difference is exactly equal to √3.

suppose the two unit vectors are a and b
such that it is possible to say

|a|=|b|=1

The magnitude of the sum of the two vectors is

|a+b|²=|a|²+|b|²+2×(a⋅b)

Similarly, the magnitude of their difference is

|a−b|²=|a|²+|b|²−2×(a⋅b)

if their sum is also a unit vector, then |a+b|=1 and thus (a⋅b)=−12

so, the magnitude of their difference is

|a−b|² = 1+1−2(−12)

=√3