Question

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

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

Answer 1

Answer: (A)

$\sqrt{3}$

$\hat{a}+\hat{b}=\hat{c},$ where magnitudes $a,b$ and $c=1$ each.

$\sqrt{a^2+b^2+2ab.cos\theta }=1$

$2+2cos\theta =1,$ giving $cos\theta =-1/2or\theta =120^0$

Thus, $|\hat{a}-\hat{b}|=\sqrt{1+1-2\times 1\times 1\times (-1/2)}=\sqrt{3}$