Question

Assertion :The vectors $\overrightarrow{A}=2\hat{i}-3\hat{j}+\hat{k}and\overrightarrow{B}=\hat{i}+\hat{j}+\hat{k}$ are mutually perpendicular. Reason: $\overrightarrow{A}\bullet \overrightarrow{B}=0$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$\overrightarrow{A}\bullet \overrightarrow{B}=(2\hat{i}-3\hat{j}+\hat{k})\bullet (\hat{i}+\hat{j}+\hat{k})$
$=\left(2\right)\left(1\right)+(-3)\left(1\right)+\left(1\right)\left(1\right)=0=AB\cos \theta$

$\therefore \cos \theta =0(asA\ne 0,B\ne 0)$
$\Rightarrow \theta ={90}^{\circ }$
Thus, the vectors are perpendicular to each other, hence assertion is correct and the reason is statement 2.