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

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

Answers (1)

Answer:

\frac{-\hat{\imath}+4 \hat{\jmath}+3 \hat{k}}{3}

Hint:

Use position vector formula.

Given:

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

Solution:

A vector divides an line Internally as in

Position vector of P and Q are given as:  \mathrm{m}: \mathrm{n}=\frac{m Q+n P}{m+n}

O \vec{P}=(\hat{\imath}+2 \hat{\jmath}+\hat{k}) \text { and } O \vec{Q}=(-\hat{\imath}+\hat{j}+\hat{k})

\frac{m}{n}=\frac{2}{1}

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

\begin{aligned} &O \vec{R}=\frac{(\hat{\imath}+2 \hat{\jmath}+\hat{k})+2(-\hat{\imath}+\hat{\jmath}+\hat{k})}{2+1}=\frac{-\hat{\imath}+4 \hat{\jmath}+3 \hat{k}}{3} \\\\ &O \vec{R}=-\frac{1}{3} \hat{\imath}+\frac{4}{3} \hat{\jmath}+\hat{k} \end{aligned}

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