answer for this sum

The position vector of point R dividing the line segment joining two points

P and Q in the ratio m: n is given by:

1. Internally:

2. Externally:

So let point C divides line segment AB internally
$\overrightarrow{OC} =\frac{3\left(2\overrightarrow{a}+4\overrightarrow{b}\right)+\left(2\overrightarrow{a}-8\overrightarrow{b}\right)}{3+1}=2\overrightarrow{a}+\overrightarrow{b}$
Now let point D divides line segment AB externally
$\overrightarrow{OD} =\frac{3\left(2\overrightarrow{a}+4\overrightarrow{b}\right)-\left(2\overrightarrow{a}-8\overrightarrow{b}\right)}{3-1}=2\overrightarrow{a}+10\overrightarrow{b}$

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