The position vector of a point that divides t | vedclass

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(B) Let the points be $\vec{p} = \hat{i} + 2\hat{j} - \hat{k}$ and $\vec{q} = -\hat{i} + \hat{j} + \hat{k}$.For external division in the ratio $m:n =

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

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(B) Let the points be $\vec{p} = \hat{i} + 2\hat{j} - \hat{k}$ and $\vec{q} = -\hat{i} + \hat{j} + \hat{k}$.For external division in the ratio $m:n = 1:2$,the position vector $\vec{r}$ is given by the formula:$\vec{r} = \frac{m\vec{q} - n\vec{p}}{m - n}$Substituting the values:$\vec{r} = \frac{1(-\hat{i} + \hat{j} + \hat{k}) - 2(\hat{i} + 2\hat{j} - \hat{k})}{1 - 2}$$\vec{r} = \frac{-\hat{i} + \hat{j} + \hat{k} - 2\hat{i} - 4\hat{j} + 2\hat{k}}{-1}$$\vec{r} = \frac{-3\hat{i} - 3\hat{j} + 3\hat{k}}{-1}$$\vec{r} = 3\hat{i} + 3\hat{j} - 3\hat{k}$

The position vector of a point that divides the line segment joining $P \equiv(1,2,-1)$ and $Q \equiv(-1,1,1)$ externally in the ratio $1: 2$ is:

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