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Provide solution for RD Sharma maths class 12 chapter Vector or Cross Product exercise 24.1 question 18

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Hint               : To solve this equation we use |\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \sin \theta

Given            : \vec{a} \times \vec{b}=\vec{c} \text { and } \vec{b} * \vec{c}=\vec{a} \text { and } \vec{c} * \vec{a}=\vec{b}

Solution      : \vec{a} \times \vec{b}=\vec{c}

\begin{aligned} &\Rightarrow \vec{a} \times \vec{b}=\vec{c} \\\\ &\Rightarrow|\vec{a}||\vec{b}| \sin \theta=\vec{c} \\\\ &\theta=\sin ^{-1}(1) \\\\ &\theta=\frac{\Pi}{2} \; 0 r \; 90^{\circ} \end{aligned}


Similarly can be prove for others


\vec{b} \times \vec{c}=\vec{a} this means perpendicular (\vec{b} \times \vec{c})

\vec{c} \times \vec{a}=\vec{b} this means perpendicular (\vec{c} \times \vec{a})

This are together \vec{a}, \vec{b} \text { and } \vec{c} form orthonormal trial

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