Find the position vector of a point R which divides the line joining in the ratio 2 : 1 (i) internally and (ii) externally. - Wired Faculty

Vector Algebra

Question

Find the position vector of a point R which divides the line joining $straight P left parenthesis 3 straight a with rightwards arrow on top space minus space 2 space straight b with rightwards arrow on top right parenthesis space and space straight Q left parenthesis straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top right parenthesis$ in the ratio 2 : 1
(i) internally and (ii) externally.

Solution

Given points are

straight P left parenthesis 3 straight a with rightwards arrow on top space minus space 2 straight b with rightwards arrow on top right parenthesis comma space space straight Q left parenthesis straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top right parenthesis

(i) The position vector of the point R dividing the join of P and Q internally in the

ratio 2 : 1 is

(ii) The position vector of the point R dividing the join of P and Q externally in the ratio 2 : 1 is

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