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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 6

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Multiple choice question 6

Answers (1)

Answer: 4 \overrightarrow{O G}

Hint: Find \overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}+\overrightarrow{O D}=?

Given: If G is intersection of diagonal of parallelogram. ABCD  and O is any point that \overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}+\overrightarrow{O D}=?

Solution: Let consider the point O as origin G is the midpoint of AC

        \begin{aligned} &\overrightarrow{O G}=\frac{\overrightarrow{O A}+\overrightarrow{O C}}{2} \\\\ &2 \overrightarrow{O G}=\overrightarrow{O A}+\overrightarrow{O C} \end{aligned}                ................(1)

Also G is midpoint of BD

        \begin{aligned} &\overrightarrow{O G}=\frac{\overrightarrow{O B}+\overrightarrow{O D}}{2} \\\\ &2 \overrightarrow{O G}=\overrightarrow{O B}+\overrightarrow{O D} \end{aligned}

On add (1) and (2)

        \begin{aligned} &2 \overrightarrow{O G}+2 \overrightarrow{O G}=\overrightarrow{O A}+\overrightarrow{O C}+\overrightarrow{O B}+\overrightarrow{O D} \\\\ &4 \overrightarrow{O G}=\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}+\overrightarrow{O D} \\\\ &\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}+\overrightarrow{O D}=4 \overrightarrow{O G} \end{aligned}

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