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Explain solution RD Sharma class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 16 maths

Answers (1)

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Answer:-2

Hint:- To solve this we use triangle law of vector addition

Given:-If A,B,C,D,E  are five point in a plane such that \overrightarrow{A B}+\overrightarrow{A E}+\overrightarrow{B C}+\overrightarrow{D C}+\overrightarrow{E D}=K \overrightarrow{A C}   then K IS….

                                            

Solution:-       

     \begin{aligned} \overrightarrow{A B}+\overrightarrow{A E}+\overrightarrow{B C}+\overrightarrow{D C}+\overrightarrow{E D} \\ \end{aligned}

\begin{aligned} &=(\overrightarrow{A B}+\overrightarrow{B C})+(\overrightarrow{E D}+\overrightarrow{D C})+\overrightarrow{A E} \\\\ &=\overrightarrow{A C}+(\overrightarrow{E C}+\overrightarrow{A E}) \end{aligned}                [∴Triangle Law of Vector Addition]

\begin{aligned} &=\overrightarrow{A C}+\overrightarrow{A C} \\\\ &=2 \overrightarrow{A C} \\\\ &\therefore K=2 \end{aligned}

 

                                                                         

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