Section formula of vectors devides internally and externally in the ratio m: n (Hindi + English) HD

Section formula of vectors : Let P and Q be two points represented by the position vectors OP and OQ, respectively,with respect to the origin O. Then the line segment joining the points P and Q may be divided by a third point, say R, in two ways – internally and externally. Here, we intend to find the position vector OR for the point R with respect to the origin O. We we are explaining each of two cases one by one. Case I When R divides PQ internally If R divides PQ such that RQm =PRn where m and n are positive scalars, we say that the point R divides PQ internally in the ratio of m : n. Now from triangles ORQ and OPR, Case II When R divides PQ externally.We leave it to the reader as an exercise to verify that the position vector of the point R which divides the line segment PQ externally in the ratio