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

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Answer:- \overrightarrow{A C}+\overrightarrow{A F}-\overrightarrow{A B}=\overrightarrow{A E}

Hint:-To solve this equation, we use reverse process of vectors

Given:-In a rectangular hexagon \text { ABCDEF, } \overrightarrow{A C}+\overrightarrow{A F}-\overrightarrow{A B}

                                    

Solution:-

we have \overrightarrow{A E}=\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{D E}                                       …(i)

From figure we can see

\begin{aligned} &\overrightarrow{A B}+\overrightarrow{B C}=\overrightarrow{A C}\quad \quad\quad\quad\quad\quad\quad...(ii)\\ \\&\overrightarrow{C D}=\overrightarrow{A F} \quad[\because A F \| C D,-A F=C D]\quad ...(iii)\\ \\&\overrightarrow{D E}=-\overrightarrow{A B}\quad\quad\quad\quad\quad\quad ...(iv) \end{aligned}

Using (ii) , (iii) and (iv) in (i), we get

\begin{aligned} &\overrightarrow{A E}=\overrightarrow{A C}+\overrightarrow{A F}-\overrightarrow{A B} \\\\ &\text { Hence } \overrightarrow{A C}+\overrightarrow{A F}-\overrightarrow{A B}=\overline{A E} \end{aligned}

 

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