#### Need solution for RD sharma maths class 12 chapter 24 vector or cross product Exercises Multiple choice questions question 15 maths textbook solution

Answer: $\frac{\pi }{4}$

Given: $\theta$is the angle between any two vectors $\overrightarrow{a}$ & $\overrightarrow{b}$$\left | \overrightarrow{a}.\overrightarrow{b} \right |=\left | \overrightarrow{a}\times \overrightarrow{b} \right |$

Hint: Using $\left | \overrightarrow{a}\times \overrightarrow{b} \right |=\left | \overrightarrow{a} \right |\left | \overrightarrow{b} \right |\sin \theta$and $\left | \overrightarrow{a}. \overrightarrow{b} \right |=\left | \overrightarrow{a} \right |\left | \overrightarrow{b} \right |\cos \theta$

Explanation: We are given

$\left | \overrightarrow{a}\times \overrightarrow{b} \right |=\left | \overrightarrow{a}.\overrightarrow{b} \right |$                                                         $\left | \overrightarrow{a}\times \overrightarrow{b} \right |=\left | \overrightarrow{a} \right |\left | \overrightarrow{b} \right |\sin \theta$  and $\left | \overrightarrow{a}. \overrightarrow{b} \right |=\left | \overrightarrow{a} \right |\left | \overrightarrow{b} \right |\cos \theta$

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

$\Rightarrow \sin \theta =\cos \theta$

Divide by $\cos \theta$

$\frac{\sin \theta }{\cos \theta }=\frac{\cos \theta }{\cos \theta }$

$\tan \theta =1\Rightarrow \theta =\frac{\pi }{4}$