# X and Y are two points with position vectors 3vec("a") + vec("b") and vec("a")-3vec("b")respectively. Write the position vector of a point Z which divides the line segment XY in the ratio 2 : 1 - Mathematics

Sum

X and Y are two points with position vectors 3vec("a") + vec("b") and vec("a")-3vec("b")respectively. Write the position vector of a point Z which divides the line segment XY in the ratio 2 : 1 externally.

#### Solution

The position vectors given are

vec("OX") = 3 vec("a") + vec("b") and vec("OY") = vec("a") - 3vec("b")

The position vector of the point Z which divides the line segment XY in the ratio 2 : 1 externally will be

vec("OZ") = (2(vec("a")-3vec("b"))-(3vec("a")+vec("b")))/(2-1) = (-vec("a")-7vec("b"))/1

⇒ vec("OZ") = -vec("a") - 7vec("b")

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