Question

If the sum of two unit vectors is a vector show that the difeerence in the their magnitude is

Answer 1

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