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Vector Algebra

Question
CBSEENMA12034033

Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q(4, 1, – 2).

Solution

Let straight a with rightwards arrow on top space and space straight b with rightwards arrow on top be position vectors of points P(2, 3, 4) and Q(4, 1, -2) respectively.
                     therefore space space space space straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 3 space straight j with hat on top space plus space 4 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space 4 space straight i with hat on top space plus space straight j with hat on top space minus space 2 space straight k with hat on top
Position vector of mid-point of PQ is
         fraction numerator straight a with rightwards arrow on top plus straight b with rightwards arrow on top over denominator 2 end fraction space straight i. straight e. comma space fraction numerator left parenthesis 2 space straight i with hat on top space plus space 3 space straight j with hat on top space plus space 4 space straight k with hat on top right parenthesis space plus space left parenthesis 4 space straight i with hat on top space plus space straight j with hat on top space minus space 2 space straight k with hat on top right parenthesis over denominator 2 end fraction
i.e. fraction numerator 6 space straight i with hat on top space plus space 4 space straight j with hat on top space plus space 2 space straight k with hat on top over denominator 2 end fraction    i.e.,  3 space straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight k with hat on top