D , E , F are respectively the points on the sides B C , C A and A B of a ∆ A B C dividing them in the ratio 2 : 3 , 1 : 2 , 3 : 1 internally. The lines B E and C F intersect on the line A D at P . If A P → = x 1 A B → + y 1 · A C → , then x 1 + y 1 =

Step-by-step solution

By using section formula we can obtain required result If vector d , e , f are position vector of points D , E & F respectively then, by section formula d → = 2 c → + 3 b → 5 . . . i e → = 2 c → + a → 3 . . . ii f → = 3 b → + a → 4 . . . iii ​​​​​​​ Equation of line A D is vector r → = a → + t d → - a → Equation of line B E is r → = b → + m e → - b → For intersection of vector A D and vector B E we need that " a → + t d →