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Vector Algebra

Question
CBSEENMA12034032
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If straight a with rightwards arrow on top an straight b with rightwards arrow on top are position vectors of points A and B respectively, then find the position vector of points of trisection of AB.

Solution
Let P and Q be the points of trisection of AB. Then P divides AB in the ration 1 : 2 and Q divides AB in the ratio 2 : 1.

     P.V. of P = fraction numerator left parenthesis 1 right parenthesis space left parenthesis straight b with rightwards arrow on top right parenthesis space plus space left parenthesis 2 right parenthesis thin space left parenthesis straight a with rightwards arrow on top right parenthesis over denominator 1 plus 2 end fraction space equals space fraction numerator 2 straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top over denominator 3 end fraction
      P.V. of Q = fraction numerator left parenthesis 2 right parenthesis space left parenthesis straight b with rightwards arrow on top right parenthesis space plus space left parenthesis 1 right parenthesis thin space left parenthesis straight a with rightwards arrow on top right parenthesis over denominator 2 plus 1 end fraction space equals fraction numerator straight a with rightwards arrow on top space plus space 2 space straight b with rightwards arrow on top over denominator 3 end fraction

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