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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 14

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 14

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Answer:-  3

Hint:-To solve this equation we do \overrightarrow{A B}=\overrightarrow{O B}-\overrightarrow{O A} method

Given:-A, B, C, D, E are five coplanar, such that \overrightarrow{D A}+\overrightarrow{D B}+\overrightarrow{D C}+\overrightarrow{A E}+\overrightarrow{B E}+\overrightarrow{C E}=K \overrightarrow{D E} \text { then } \mathrm{k} \text { is.... }

Solution:- \overrightarrow{A B}=\overrightarrow{O B}-\overrightarrow{O A}

\overrightarrow{D A}+\overrightarrow{D B}+\overrightarrow{D C}+\overrightarrow{A E}+\overrightarrow{B E}+\overrightarrow{C E}=K \overrightarrow{D E}

\begin{aligned} &\Rightarrow(\overrightarrow{O A}-\overrightarrow{O D})+(\overrightarrow{O B}-\overrightarrow{O D})+(\overrightarrow{O C}-\overrightarrow{O D})+(\overrightarrow{O E}-\overrightarrow{O A})+(\overrightarrow{O E}-\overrightarrow{O B})+(\overrightarrow{O E}-\overrightarrow{O C})=k \overrightarrow{D E} \\\\ &\Rightarrow 3(\overrightarrow{O E}-\overrightarrow{O D})=k \overrightarrow{D E} \\ \end{aligned}

\Rightarrow 3 \overrightarrow{D E}=k \overrightarrow{D E} \\

\Rightarrow 3=k \\

\Rightarrow k=3

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