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The-points-A-B-and-C-have-position-vectors-a-b-and-c-respectively-reffrred-to-an-origin-O-i-Given-that-the-point-X-lie-on-AB-produced-so-that-AB-BX-2-1-find-x-the-position-vector-of-X-in-terms




Question Number 174489 by pete last updated on 02/Aug/22
The points A, B and C have position vectors  a, b and c respectively reffrred to an origin O.  i. Given that the point X lie on AB produced  so that AB : BX=2:1, find x, the position  vector of X in terms of b and c.  ii. if Y lies on BC, between B and C so that  BY : YC = 1:3, find y, the position vector  of Y in terms of b and c.  iii. Given that Z  is the mid point of AC,   show that X, Y and Z are collinear.
ThepointsA,BandChavepositionvectorsa,bandcrespectivelyreffrredtoanoriginO.i.GiventhatthepointXlieonABproducedsothatAB:BX=2:1,findx,thepositionvectorofXintermsofbandc.ii.ifYliesonBC,betweenBandCsothatBY:YC=1:3,findy,thepositionvectorofYintermsofbandc.iii.GiventhatZisthemidpointofAC,showthatX,YandZarecollinear.

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