Question

If the sum of two unit vectors is a unit vector, then the
magnitude of their difference is
(a) √3 (b) √2
(c) √5 (d) 1/√2

Answer 1

Answer:

a) √3

Explanation:

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

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

option a) is correct