Write the Position Vector of the Point Which Divides the Join of Points with Position Vectors - Mathematics

Write the position vector of the point which divides the join of points with position vectors 3veca-2vecb and 2veca+3vecb in the ratio 2 : 1.

Solution

Suppose R be the point which divides the line joining the points with position vectors 3veca-2vecb and 2veca+3vecb in the ratio 2 : 1.

and vec(OA)=3veca-2vecb  and vec(OB)=2veca+3vecb

Here, m : n = 2 : 1

Therefore, position vector vec(OR) is as follows

vec(OR)=(mvec(OB)+nvec(OA))/(m+n)

=(2(2veca+3vecb)+1(3 veca-2 vecb))/(2+1)

=(7 vec a+4vecb)/3

=7/3 veca+4/3 vec b

Concept: Basic Concepts of Vector Algebra
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