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  • Please solve RD Sharma class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 13 maths textbook solution

Please solve RD Sharma class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 13 maths textbook solution

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Answer: 1

Hint:-To solve this equation, we split  \overline{O A} \text { in } a, b, c forms

Given:-If O,A,B,C and \; Dare five points 3 \overrightarrow{O D}+\overrightarrow{D A}+\overrightarrow{D B}+\overrightarrow{D C}=k(\overline{O A}+\overrightarrow{O B}+\overrightarrow{O C}) \text { then } \mathrm{k}=____

Solution: O=\vec{o}, A=\vec{a}, B=\vec{b}, C=\vec{c}, D=\vec{d}

\begin{aligned} &3 \overrightarrow{O D}+\overrightarrow{D A}+\overrightarrow{D B}+\overrightarrow{D C}=k(\overline{O A}+\overrightarrow{O B}+\overrightarrow{O C}) \\\\ &3(d-o)+(a-d)+(b-d)+(c-d)=k[(a-o)+(b-o)+(c-o)] \end{aligned}

\begin{aligned} &3 d-3 o+a-d+b-d+c-d=k(a-o+b-o+c-o) \\\\ &(-30+a+b+c)=k(-3 o+a+b+c) \\\\ &k=1 \end{aligned}

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