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Vector Algebra

Question
CBSEENMA12034034

Find the vector from the origin O to the centroid of the triangle whose vertices are (1, – 1, 2), (2, 1, 3) and (–1, 2, –1).

Solution

Let straight a with rightwards arrow on top space equals space straight i with hat on top space minus space straight j with hat on top space plus space 2 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight j with hat on top space plus space 3 space straight k with hat on top comma space space straight c with rightwards arrow on top space equals space minus straight i with hat on top space plus space 2 space straight j with hat on top space minus space straight k with hat on top be the position vectors of vertices A, B, C respectively. 
Position vector straight d with rightwards arrow on top of centroid is given by
 straight d with rightwards arrow on top space equals space fraction numerator straight a with rightwards arrow on top plus straight b with rightwards arrow on top plus straight c with rightwards arrow on top over denominator 3 end fraction
space space space space space space equals space fraction numerator left parenthesis straight i with hat on top space minus space straight j with hat on top space plus space 2 space straight k with hat on top right parenthesis space plus space left parenthesis 2 space straight i with hat on top space space plus space straight j with hat on top space plus 3 space straight k with hat on top right parenthesis space plus space left parenthesis negative straight i with hat on top space plus space 2 space straight j with hat on top space minus space straight k with hat on top right parenthesis over denominator 3 end fraction space equals space fraction numerator 2 stack straight i space with hat on top plus 2 space straight j with hat on top space plus space 4 space straight k with hat on top over denominator space 3 end fraction