Question

if the sum of two unit vector is also a unit vector then magnitude of their difference and angle between the two unit vector 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