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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
Question
Write the position vector of the point which divides the join of points with position vectors $3\overrightarrow{\text{a}} - 2\overrightarrow{\text{b}} \text{and } 2\overrightarrow{\text{a}} + 3\overrightarrow{\text{b}}$ in the ratio $2:1.$
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Answer

$\frac{2(2\overrightarrow{\text{a}}+3\overrightarrow{\text{b}})+1 (3\overrightarrow{\text{a}} - 2\overrightarrow{\text{b}})}{2 +1} $
$= \frac{7}{3}\overrightarrow{\text{a}} + \frac{4}{3}\overrightarrow{\text{b}}$

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