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  • Explain solution RD Sharma class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 8 maths

Explain solution RD Sharma class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 8 maths

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Answer: \vec{b}+\vec{c}

Hint: Find \overrightarrow{A E}

Given: In regular Hexagon  \text { ABCDEF, } \overrightarrow{A B}=\vec{a}, \overrightarrow{B C}=\vec{b}, \overrightarrow{C D}=\vec{c} then \overrightarrow{A E}=?

Solution: We have

         \overrightarrow{A B}=\vec{a}, \overrightarrow{B C}=\vec{b}, \overrightarrow{C D}=\vec{c}

   

         \overrightarrow{A C}=a+b

In \Delta ACD we have      

        \begin{aligned} &\overrightarrow{A C}+\overrightarrow{C D}=\overrightarrow{A D} \\ &\vec{a}+\vec{b}+\vec{c}=\overrightarrow{A D} \end{aligned}

In \Delta AED we have

        \begin{aligned} &\overrightarrow{A D}+\overrightarrow{D E}=\overrightarrow{A E} \\\\ &a+b+c-a=\overrightarrow{A E} \\\\ &\overrightarrow{A E}=\vec{b}+\vec{c} \end{aligned} \quad(D E=B A=-a)

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