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  • Please solve RD Sharma class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 9 maths textbook solution

Please solve RD Sharma class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 9 maths textbook solution

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Answer: \alpha+\beta+\gamma=1

Hint: Find plane of vector equation

Given: The vector equation of plane passing through  \vec{a}, \vec{b}, \vec{c}, \vec{r}=\alpha \vec{a}+\beta \vec{b}+\gamma \vec{c} provide that

Solution: \vec{r}=\alpha \vec{a}+\beta \vec{b}+\gamma \vec{c}            ................(1)

            \begin{aligned} &\vec{r}=\vec{a}+\lambda_{1} \vec{a}+\lambda_{1} \vec{c}-\lambda_{1} \vec{b}-\lambda_{2} \vec{a}\\\\ &\vec{r}=\vec{a}\left(\lambda_{1}-\lambda_{2}\right)+\vec{b}\left(-\lambda_{1}\right)+\lambda_{2} \vec{c} \end{aligned}        ..............(2)

By comparing (1) and (2)

        \begin{aligned} &\alpha+\beta+\gamma=1+\lambda_{1}-\lambda_{2}-\lambda_{1}+\lambda_{2} \\ \\ &\alpha+\beta+\gamma=1 \end{aligned}

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