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  • Explain solution RD Sharma class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 20 maths

Explain solution RD Sharma class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 20 maths

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Answer:- 0

Hint:- To solve this equation we use mid-point formula

Given:-The algebraic sum of the vector directed from the vectors to the mid points of the opposite side is equal to

Solution:-

\begin{aligned} &\text { } \overrightarrow{A D}+\overrightarrow{B \bar{E}}+\overrightarrow{C \vec{F}}\\\\ &\text { In } \Delta A B D\; \; \overrightarrow{A B}+\overrightarrow{B D}+\overrightarrow{D A}=0 \end{aligned}

\begin{aligned} &\overrightarrow{E C}=\frac{1}{2} \overrightarrow{A C} \\\\ &\overrightarrow{B D}=\frac{1}{2} \overrightarrow{B C} \\\\ &\overrightarrow{F B}=\frac{1}{2} \overrightarrow{A B} \end{aligned}

\begin{aligned} &\therefore \overrightarrow{A D}=\overrightarrow{A B}+\frac{1}{2} \overrightarrow{B C} \\\\ &\text { In } \Delta B E C \; \; \overrightarrow{B C}+\overrightarrow{C E}+\overrightarrow{E B}=0 \end{aligned}

\begin{aligned} &\therefore \overrightarrow{B E}=\overrightarrow{B C}+\frac{1}{2} \overrightarrow{C A} \\\\ &\text { In } \Delta A C F \overrightarrow{A F}+\overrightarrow{F C}+\overrightarrow{C A}=0 \\\\ &\therefore \overrightarrow{C F}=\overrightarrow{C A}+\frac{1}{2} \overrightarrow{A B} \end{aligned}

\begin{aligned} &\overrightarrow{A B}+\frac{1}{2} \overrightarrow{B C}+\overrightarrow{B C}+\frac{1}{2} \overrightarrow{C A}+\overrightarrow{C A}+\frac{1}{2} \overrightarrow{A B} \\\\ &\Delta A B C \\\\ &\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}=0 \end{aligned}

\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}+\frac{1}{2}(\overrightarrow{B C}+\overrightarrow{C A}+\overrightarrow{A B})=0

 

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