Let position vectors of point A,B and C are a,b and c .Point D divides line segment BC internally in the ratio 2:1 . Find vector AD

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Solution

$L e t t h e p o s i u t i o n v e c t o r o f p o i n t D b e \vec{d} U \sin g s e c t i o n f o r m u l a I f Q \vec{(q)} d i v i d e s l i n e s e g m e n t j o i n i n g P \vec{(p)} a n d R \vec{(r)} i n t h e r a t i o m : n t h e n \vec{q} = \frac{m \vec{r} + n \vec{p}}{m + n} \vec{d} = \frac{2 \vec{c} + \vec{b}}{3} V e c t o r A D = \vec{d} - \vec{a} = \frac{2 \vec{c} + \vec{b}}{3} - \vec{a} = \frac{2 \vec{c} + \vec{b} - 3 \vec{a}}{3}$

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Let position vectors of point A,B and C are a,b and c .Point D divides line segment BC internally in the ratio 2:1 . Find vector AD

Let the posiution vector of point D be d→Using section formulaIf Qq→ divides line segment joining Pp→ and Rr→ in the ratio m:n then q→=mr→+np→m+nd→=2c→+b→3Vector AD=d→-a→=2c→+b→3-a→=2c→+b→-3a→3