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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

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

Answers (1)

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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