Find the position vector of a point which divides the join of points with position vectors a−2b and 2a+b externally in the ratio 2 : 1 - Mathematics

Question

Find the position vector of a point which divides the join of points with position vectors $\vec{a} - 2 \vec{b} and 2 \vec{a} + \vec{b}$ externally in the ratio 2 : 1

Solution

Let A and B be the points with position vectors $\vec{a} - 2 \vec{b} and 2 \vec{a} + \vec{b}$ respectively.

Also, let R divide AB externally in the ratio 2 : 1.

$∴ Position vector of R = \frac{2 \times (2 \vec{a} + \vec{b}) - 1 \times (\vec{a} - 2 \vec{b})}{2 - 1} = 3 \vec{a} + 4 \vec{b}$

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Basic Concepts of Vector Algebra

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Find the position vector of a point which divides the join of points with position vectors a−2b and 2a+b externally in the ratio 2 : 1 - Mathematics

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