Question

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is :

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $1/\sqrt{2}$
• D. $\sqrt{5}$

Answer 1

The correct option is B $\sqrt{3}$

Resultant vector of two vectors A and B R=$\sqrt{A^2+B^2+2ABcos\theta }$

Here A,B,R are unit vectors

1=$\sqrt{1^2+1^2+2\times 1\times 1cos\theta }$

$\theta =\frac{-\pi }{3}$

X=|A-B|

X=$\sqrt{1^2+1^2-2\times 1\times 1cos\theta }=\sqrt{3}$