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

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Answer: \frac{\pi }{4}

Given: \thetais 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 \thetaand \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}

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