Question

if sum of two unit vector is a unit vector then magnitude of difference is

Answer 1

under root(3)..........

Answer 2

Let the two unit vectors be a→a→ and b→b→

Given |a→+b→|=1|a→+b→|=1

⇒|a→+b→|2=1⇒|a→+b→|2=1

⇒|a→|2+|b→|2+2a→.b→=1⇒|a→|2+|b→|2+2a→.b→=1

⇒2a→.b→=−1⇒2a→.b→=−1

|a→−b→|2=|a→|2+|b→|2−2a→.b→|a→−b→|2=|a→|2+|b→|2−2a→.b→

=2+1=3=2+1=3

∴|a→−b→|=√3