Question

If $|\overline{x}|=|\overline{y}|=1$ and $\overline{x}\perp \overline{y}$, then $|\overline{x}-\overline{y}|=$ _____________.

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $1$
• D. $0$

Answer 1

The correct option is A $\sqrt{2}$

Here we have $|\overline{x}|=|\overline{y}|=1$ and $\overline{x}\perp \overline{y}$
$\therefore \overline{x}\cdot \overline{y}=0$ ..$\left(1\right)$
Now $|\overline{x}-\overline{y}{|}^2$
$=(\overline{x}-\overline{y})\cdot (\overline{x}-\overline{y})$
$=\overline{x}\cdot \overline{x}-\overline{y}\cdot \overline{x}-\overline{x}\cdot y+\overline{y}\cdot \overline{y}$
$=|\overline{x}{|}^2-0-0+|\overline{y}{|}^2$
$=1+1$
$=2$
$\therefore |\overline{x}-\overline{y}|=\sqrt{2}$.