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  • Please solve RD Sharma class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 17 maths textbook solution

Please solve RD Sharma class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 17 maths textbook solution

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Answer:-\lambda =4

Hint:-To solve this question we have to connect or add AP,BP ,CP\; and\; DP vectors

Given:-Let P be the point of intersection of the diagonal of a parallelogram ABCD and O is any point If \overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}+\overrightarrow{O D}=\lambda \overrightarrow{O P}            

Solution:-   

\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}+\overrightarrow{O D}=\lambda \overline{O P}

\begin{aligned} &=(\overrightarrow{O A}+\overrightarrow{A P})+(\overrightarrow{O B}+\overrightarrow{B P})+(\overrightarrow{O C}-\overrightarrow{C P})+(\overrightarrow{O D}+\overrightarrow{D P}) \\\\ &=\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}+(\overrightarrow{A P}+\overline{C P})+(\overline{B P}+\overrightarrow{D P}) \\\\ &=\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}+\overrightarrow{O D}=4 \overline{O P} \\\\ &\lambda=4 \end{aligned}       

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