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  • Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 23

Need solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 23

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Answer:-2 \hat{i}-\hat{j}+\hat{k}

Hint:-To solve this equation we use standard formula.

Given:-The position vectors of two points A and B are \overrightarrow{O A}=2 \hat{i}-\hat{j}-\hat{k} \text { and } \overrightarrow{O B}=2 \hat{i}-\hat{j}+2 \hat{k}  respectively. The position vectors of a point Pwhich divides the line segment joining A and B in the ratio 2:1 is ----

Solution:- \vec{a}=2 \hat{i}-\hat{j}-\hat{k}

                                            

\begin{aligned} &\vec{b}=2 \hat{i}-\hat{j}+2 \hat{k} \\\\ &m=2 ; n=1 \end{aligned}

Section formula:

Internal   =\frac{m \vec{b}+n \vec{a}}{m+n}

\begin{aligned} &\Rightarrow \frac{m \vec{b}+n \vec{a}}{m+n} \\\\ &=\frac{2(2 \hat{i}-\hat{j}+2 \hat{k})+1(2 \hat{i}-\hat{j}-\hat{k})}{2+1} \end{aligned}

\begin{aligned} &=\frac{4 \hat{i}-2 \hat{j}+4 \hat{k}+2 \hat{i}-\hat{j}-\hat{k}}{3} \\\\ &=\frac{6 \hat{i}-3 \hat{j}+3 \hat{k}}{3} \\\\ &=2 \hat{i}-\hat{j}+\hat{k} \end{aligned}

 

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