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Vector Algebra

Question
CBSEENMA12033992
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Find the unit vector in the direction of the sum of the vectors straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 2 space straight j with hat on top space minus space 5 space straight k with hat on top space and space space straight b with rightwards arrow on top space equals space 2 straight i with hat on top space plus space straight j with hat on top space plus 3 space straight k with hat on top

Solution

             straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 2 space straight j with hat on top space minus space 5 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space 2 straight i with hat on top space plus space straight j with hat on top space plus 3 space straight k with hat on top
therefore space space space space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space equals space 4 space straight i with hat on top space plus space 3 space straight j with hat on top space minus space 2 space straight k with hat on top therefore space space space space open vertical bar straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 4 right parenthesis squared plus left parenthesis 3 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared end root space equals space square root of 16 plus 9 plus 4 end root space equals space square root of 29 therefore space space space space unit space vector space in space the space direction space of space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space space space space space space space space space space space space space space space equals space fraction numerator straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close vertical bar end fraction space equals space fraction numerator 1 over denominator square root of 29 end fraction left parenthesis 4 straight i with hat on top space plus space 3 space straight j with hat on top space minus space 2 space straight k with hat on top right parenthesis space space space space space space space space space space space space space space space equals space fraction numerator 4 over denominator square root of 29 end fraction straight i with hat on top space plus space fraction numerator 3 over denominator square root of 29 end fraction straight j with hat on top space minus space fraction numerator 2 over denominator square root of 29 end fraction straight k with hat on top

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