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Find the Position Vector of the Point Which Divides the Join of Points with Position Vectors → a + 3 → B and → a − → B Internally in the Ratio 1 : 3. - Mathematics

Sum

Find the position vector of the point which divides the join of points with position vectors `vec"a" + 3vec"b" and vec"a"- vec"b"` internally in the ratio 1 : 3. 

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Solution

Required position vector is `(1(vec"a" - vec"b") + 3(vec"a" + 3vec"b"))/(1 + 3)`

= `(1(vec"a" - vec"b") + 3(vec"a" + 3vec"b"))/(4)`

= `vec"a" + 2vec"b"`.

Concept: Position Vector of a Point Dividing a Line Segment in a Given Ratio
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