Question

Write True/False in the following statement:
Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular if $\overrightarrow{a}\cdot \overrightarrow{b}=0$

• A. True
• B. False

Answer 1

The correct option is A True

As we know that,

$\overrightarrow{a}\cdot \overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \theta$

$\because \overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular, i.e.,

$\theta =90°$

$\therefore \overrightarrow{a}\cdot \overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos 90°$

$\Rightarrow \overrightarrow{a}\cdot \overrightarrow{b}=0(\because \cos 90°=0)$

Hence the given statement is true.