Question

If the sum of two unit vectors is also a vector of unit magnitude, the
magnitude of the difference of the two unit vectors is
1) 1 unit
2) 2 units
3) v3 units 4) zero​

Answer 1

Let the two unit vectors be a→ and b→

Given |a→+b→|=1

⇒|a→+b→|2=1

⇒|a→|2+|b→|2+2a→.b→=1

⇒2a→.b→=−1

|a→−b→|2=|a→|2+|b→|2−2a→.b→

=2+1=3

∴|a→−b→|=3–√