Question

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two non zero vectors then $|\overrightarrow{a}-\overrightarrow{b}|$ is

• A. $\ge (|\overrightarrow{a}|+|\overrightarrow{b}|{)}^2$
• B. $\ge |\overrightarrow{a}|+|\overrightarrow{b}|$
• C. $\le |\overrightarrow{a}|+|\overrightarrow{b}|$
• D. Both ($A$) and ($B$)

Answer 1

The correct option is C $\le |\overrightarrow{a}|+|\overrightarrow{b}|$

$|a-b|=\sqrt{a^2+b^2-2\overline{a}\cdot \overline{b}}$
$=\sqrt{(|a|+|b|{)}^2-2|a||b|-2\overline{a}\cdot \overline{b}}$
$\le |a|+|b|$