Question

If $|\overline{x}|=|\overline{y}|=|\overline{x}+\overline{y}|=1$ then $|\overline{x}-\overline{y}|$= __________

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

Answer 1

Answer: (B)

$\sqrt{3}$

$|\overrightarrow{x}|=x$ and $|\overrightarrow{y}|=y$

And,$x=y=1$

$|\overrightarrow{x}+\overrightarrow{y}{|}^2=1$

$⟹x^2+y^2+2xy\cos \theta =1$

$⟹2+2\cos \theta =1$

$⟹\cos \theta =\frac{-1}{2}$

Now,

$|\overrightarrow{x}-\overrightarrow{y}{|}^2=x^2+y^2-2xy\cos \theta$

$⟹|\overrightarrow{x}-\overrightarrow{y}|-2-2\cos \theta =2+1=3$

$⟹|\overrightarrow{x}-\overrightarrow{y}|=\sqrt{3}$