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  • Provide solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 14

Provide solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 14

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Answer         :\frac{\pi }{4}

Hint               : To solve this equation we use aband |\vec{a}||\vec{b}| \text { and }|\vec{a} \times \vec{b}|

Given            : |\vec{a} \times \vec{b}|=\vec{a} \cdot \vec{b}

Solution        :

                        1)\vec{a} \times \vec{b}|=|a||b| \cos \theta\\

                        2) \vec{a} \cdot \vec{b}|=|a||b| \sin \theta

\Rightarrow|\vec{a}||\vec{b}| \cos \theta=|\vec{a}||\vec{b}| \sin \theta

\begin{aligned} &\Rightarrow \frac{\sin \theta}{\cos \theta}=1 \\\\ &\Rightarrow \tan \theta=1 \\\\ &\Rightarrow \theta=\tan ^{-1} 1 \\\\ &\theta=\frac{\pi}{4} \end{aligned}

 

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