Find the projection of the vector $straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 3 straight j with hat on top space plus space 2 straight k with hat on top$ on the vector $straight b with rightwards arrow on top space equals straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight k with hat on top$ .

Solution

straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space 3 space straight j with hat on top space plus space 2 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals 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

straight a space equals square root of 4 plus 9 plus 4 end root space equals square root of 17 comma space space space straight b space equals space square root of 1 plus 4 plus 1 end root space equals space square root of 6

Projection of

straight a with rightwards arrow on top space on space straight b with rightwards arrow on top space equals space fraction numerator straight a with rightwards arrow on top. space straight b with rightwards arrow on top over denominator straight b end fraction space equals space fraction numerator left parenthesis 2 right parenthesis thin space left parenthesis 1 right parenthesis space plus space left parenthesis 3 right parenthesis thin space left parenthesis 2 right parenthesis space plus space left parenthesis 2 right parenthesis thin space left parenthesis 1 right parenthesis over denominator square root of 6 end fraction

equals space fraction numerator 2 plus 6 plus 2 over denominator square root of 6 end fraction space equals fraction numerator 10 over denominator square root of 6 end fraction space equals 5 over 3 square root of 6

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