P and Q are two points with position vectors 3 a - 2 b and a + b … - Vidyadip

Question

P and Q are two points with position vectors 3$\overrightarrow{\text{a}}$ - 2$\overrightarrow{\text{b}}$ and $\overrightarrow{\text{a}} + \overrightarrow{\text{b}}$respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2:1 externally.

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Answer

If $\overrightarrow{\text{r}}$is the position vector of R then by section formula
$\overrightarrow{\text{r}} = \frac{2(\overrightarrow{\text{a}} + \overrightarrow{\text{b}} )-1.(3\overrightarrow{\text{a}} - 2 \overrightarrow{\text{b}})}{2-1}$

$ = \frac{2\overrightarrow{\text{a}}+ 2\overrightarrow{\text{b}} - 3\overrightarrow{\text{a}} + 2 \overrightarrow{\text{b}}}{1} = 4 \overrightarrow{\text{b}} - \overrightarrow{\text{a}}.$

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