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Question
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")`
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