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Question

(A) The position vector of point $R$ dividing the line segment joining two points $P$ and $Q$ with position vectors $\vec{a}$ and $\vec{b}$ in the rat

Vedclass · Accepted Answer

$-3 \hat{i}+3 \hat{k}$

Vedclass · Answer

(A) The position vector of point $R$ dividing the line segment joining two points $P$ and $Q$ with position vectors $\vec{a}$ and $\vec{b}$ in the ratio $m: n$ externally is given by: $\vec{r} = \frac{m \vec{b} - n \vec{a}}{m - n}$.Given position vectors are $\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}$ and $\vec{b} = -\hat{i} + \hat{j} + \hat{k}$ with ratio $m: n = 2: 1$.Substituting the values into the formula:$\vec{r} = \frac{2(-\hat{i} + \hat{j} + \hat{k}) - 1(\hat{i} + 2 \hat{j} - \hat{k})}{2 - 1}$$= \frac{-2 \hat{i} + 2 \hat{j} + 2 \hat{k} - \hat{i} - 2 \hat{j} + \hat{k}}{1}$$= -3 \hat{i} + 3 \hat{k}$.

Find the position vector of a point $R$ which divides the line joining two points $P$ and $Q$ whose position vectors are $\hat{i}+2 \hat{j}-\hat{k}$ and $-\hat{i}+\hat{j}+\hat{k}$ respectively,in the ratio $2: 1$ externally.

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