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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 2

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 2

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Answer: \vec{b}-\vec{a}

Hint: AD=2BC

Given: If  \vec{a}, \vec{b} are vector forming consecutive side of rectangular Hexagon ABCDEF the vector representing side CD is                                                                           

Solution: Let ABCDEF be rectangular Hexagon such that                             

            \overrightarrow{A B}=\vec{a} \text { and } \overrightarrow{B C}=\vec{b}                                                                                  

            We know                                                                                            

           AD is parallel BC such that AD = 2BC     

            \overrightarrow{A D}=2 \overrightarrow{B C}=2 \vec{b}               

In \Delta ABC, we know

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

In \Delta ACD, we have

            \begin{aligned} &\overrightarrow{A C}+\overrightarrow{C D}=\overrightarrow{A D} \\\\ &\overrightarrow{C D}=\overrightarrow{A D}-\overrightarrow{A C} \\\\ &\overrightarrow{C D}=2 \vec{b}-(\vec{a}+\vec{b}) \\\\ &\overrightarrow{C D}=\vec{b}-\vec{a} \end{aligned}

 

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