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The position vectors of two points A and B are vector (2a + b) and (a - 3b) respectively. Find the position vector of a point C which divides AB externally in the ratio 1 : 2. Also, show that A is the mid-point of the line segment CB.

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 \(\vec{A}=2\vec{a}+\vec{b}\)

 \(\vec{B}=\vec{a}-3\vec{b}\)

Formula to be used – The point dividing a line joining points a and b in a ratio m:n internally or externally is given by \(\frac{mb±na}{m+b}\) respectively.

The position vector of the point C dividing the line externally

A is the midpoint of B and C.

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