Question

If the sum of two unit vectors is also a unit vector. Then the magnitude of their difference is:

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

Answer 1

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

Let the vectors be $a$ and $b$.

Hence, magnitude of $(\overrightarrow{a}+\overrightarrow{b})=\sqrt{(a^2+b^2+2abcosx)}=1$

$1+1+2cosx=1$

$cosx=-1/2$

Hence, difference in magnitude of $(\overrightarrow{a}-\overrightarrow{b})$

$=\sqrt{(a^2+b^2-2abcosx)}=\sqrt{(1+1-2\times 1\times 1\times -1/2)}=\sqrt{(1+1+1)}=\sqrt{3}$