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

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

Answers (1)

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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