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Vector Algebra

Question
CBSEENMA12033994
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Find the unit vector in the direction of the vector straight a with rightwards arrow on top space equals space straight i with hat on top space plus space straight j with hat on top space plus space 2 space straight k with hat on top.

Solution

   straight a with rightwards arrow on top space equals space straight i with hat on top space plus space straight j with hat on top space plus space 2 straight k with hat on top
therefore space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 1 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root space equals space square root of 1 plus 1 plus 4 end root space equals space square root of 6 therefore space space space space space unit space vector space in space the space direction space of space straight a with rightwards arrow on top space space space space space space space space space space space space space space space space space space 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 over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction space equals space fraction numerator 1 over denominator square root of 6 end fraction left parenthesis straight i with hat on top space plus space straight j with hat on top space plus 2 space straight k with hat on top right parenthesis space equals space fraction numerator 1 over denominator square root of 6 end fraction straight i with hat on top space plus space fraction numerator 1 over denominator square root of 6 end fraction straight j with hat on top space plus space fraction numerator 2 over denominator square root of 6 end fraction straight k with hat on top

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