L and M are two points with position vectors | vedclass

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(C) Given the position vectors of points $L$ and $M$ are $\vec{l} = 2\vec{a} - \vec{b}$ and $\vec{m} = \vec{a} + 2\vec{b}$ respectively.Point $N$ divi

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$5 \vec{b}$

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(C) Given the position vectors of points $L$ and $M$ are $\vec{l} = 2\vec{a} - \vec{b}$ and $\vec{m} = \vec{a} + 2\vec{b}$ respectively.Point $N$ divides the line segment $LM$ externally in the ratio $m:n = 2:1$.The formula for the position vector of a point dividing a line segment externally is $\vec{n} = \frac{m\vec{m} - n\vec{l}}{m - n}$.Substituting the values,we get:$\vec{n} = \frac{2(\vec{a} + 2\vec{b}) - 1(2\vec{a} - \vec{b})}{2 - 1}$$\vec{n} = \frac{2\vec{a} + 4\vec{b} - 2\vec{a} + \vec{b}}{1}$$\vec{n} = 5\vec{b}$.

$L$ and $M$ are two points with position vectors $2 \vec{a}-\vec{b}$ and $\vec{a}+2 \vec{b}$ respectively. The position vector of the point $N$ which divides the line segment $LM$ in the ratio $2:1$ externally is

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