Question

Assertion :The angle between the two vectors $(\hat{i}+\hat{j})$ and $(\hat{j}+\hat{k})$ is $\frac{\pi }{3}$ radian. Reason: Angle between two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ given by $\theta =co{s}^{-1}\left(\frac{\overrightarrow{A}.\overrightarrow{B}}{AB}\right)$.

• 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. Assertion is incorrect but Reason is correct

Answer 1

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

$\overrightarrow{A}=\hat{i}+\hat{j}$ and $\overrightarrow{B}=\hat{j}+\hat{k}$
$A=\sqrt{2},B=\sqrt{2}$
$\theta ={\cos }^{-1}\left(\frac{\overrightarrow{A}.\overrightarrow{B}}{AB}\right)={\cos }^{-1}\left(\frac{1}{2}\right)$.
or, $\theta ={\cos }^{-1}\left(\cos \frac{\pi }{3}\right)=\frac{\pi }{3}$
Therefore, both Assertion and Reason are correct and Reason is the correct explanation for Assertion.