Question

Statement -1: The angle between the two vectors $(\hat{i}+\hat{j})$ and $\left(\hat{k}\right)$ is $\frac{\pi }{2}$ radian.
Statement -2: Angle between two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is given by $\theta ={\cos }^{-1}\left(\frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|}\right)$

• A. Statement - 1 is True, Statement -2 is True;
  Statment -2 is a correct explanation for Statement -1
• B. Statement -1 is True, Statement -2 is True;
  Statement - 2 is NOT a correct explanation for Statement -1
• C. Statement - 1 is True, Statement - 2 is False
• D. Statement - 1 is False, Statement - 2 is True

Answer 1

The correct option is A Statement - 1 is True, Statement -2 is True;

Statment -2 is a correct explanation for Statement -1
Statement-1:
Let, $\overrightarrow{A}=\hat{i}+\hat{j}$ and $\overrightarrow{B}=\hat{k}$
So, $\overrightarrow{A}.\overrightarrow{B}=|\overrightarrow{A}||\overrightarrow{B}|\cos \theta$
$\Rightarrow (\hat{i}+\hat{j}).\left(\hat{k}\right)=1\times 1\times \cos \theta$
$\Rightarrow 0=\cos \theta$
$\Rightarrow \theta =\frac{\pi }{2}$

Statement - 2:
$\overrightarrow{A}.\overrightarrow{B}=|\overrightarrow{A}||\overrightarrow{B}|\cos \theta$
$\cos \theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|}$