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

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

Answers (1)

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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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