if the sum of two unit vectors is the unit vector then prove that the magnitude of their difference is root 3

let two vectors are a,b then

resultant of sum = (a² + b² + 2abcos@)^1/2 = 1  (given)

a = b = 1  (unit vector)

 1+1+2cos@ = 1

  cos@ = -1/2  .................1

now resultant of difference = magnitude (a-b)

R = (a² + b² - 2abcos@)^1/2

a = b = 1 , cos@ = -1/2 so

R = [ 1+1+1]^1/2 = root3