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Vector Algebra

Question
CBSEENMA12033997
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Find a vector in the direction of vector 5 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 which has magnitude 8 units. 

Solution

Let straight a with rightwards arrow on top space equals space 5 straight i with hat on top space minus 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 5 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root space equals space square root of 25 plus 1 plus 4 end root space equals space square root of 30
Unit vector along straight a with rightwards arrow on top is 
                        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 30 end fraction left parenthesis 5 straight i with hat on top space minus space straight j with hat on top space plus space 2 straight k with hat on top right parenthesis
Required vector = 8 space open parentheses 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 close parentheses space equals space fraction numerator 8 over denominator square root of 30 end fraction left parenthesis 5 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 right parenthesis
                         equals space fraction numerator 40 over denominator square root of 30 end fraction straight i with hat on top space minus space fraction numerator 8 over denominator square root of 30 end fraction straight j with hat on top space plus space fraction numerator 16 over denominator square root of 30 end fraction straight k with hat on top

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