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  • Explain solution RD Sharma class 12 Chapter 22 Algebra of Vectors Exercise 22.6 question 10 subquestion (ii)

Explain solution RD Sharma class 12 Chapter 22 Algebra of Vectors Exercise 22.6 question 10 subquestion (ii)

Answers (1)

Answer:

-3 \hat{\imath}+\hat{k}

Hint:

Use position vector formula.

Given:

P(\hat{\imath}+2 \hat{\jmath}+\hat{k}) \text { and } Q(-\hat{\imath}+\hat{\jmath}+\hat{k})  i the ratio 2:1

Solution:

Position vector of P and Q are given as:

\begin{aligned} &O \vec{P}=(\hat{\imath}+2 \hat{\jmath}+\hat{k}) \text { and } O \vec{Q}=(-\hat{\imath}+\hat{\jmath}+\hat{k}) \\\\ &\frac{m}{n}=\frac{2}{1} \end{aligned}

 

The position vector of point R which divides the line joining two points P and Q externally in the ratio 2 : 1 is given by:

 

A vector divides an line Internally as in m:n  Externally  =\frac{m \vec{Q}-n \vec{p}}{m-n}

\begin{aligned} &O \vec{R}=\frac{(\hat{\imath}+2 \hat{\jmath}+\hat{k})-2(-\hat{\imath}+\hat{\jmath}+\hat{k})}{1-2}=\frac{3 \hat{\imath}-\hat{k}}{-1} \\\\ &O \vec{R}=-3 \hat{\imath}+\hat{k} \end{aligned}

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