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Vector Algebra

Question
CBSEENMA12033996
Wired Faculty App

If straight a with rightwards arrow on top space equals straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top,    straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space plus space 3 space straight k with hat on top and straight c with rightwards arrow on top space equals space straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top, find a vector parallel to the vector 2 space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space plus space 3 space straight c with rightwards arrow on top.

Solution

       straight a with rightwards arrow on top space equals space straight i with hat on top plus straight j with hat on top plus straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 2 straight i with hat on top space minus space straight j with hat on top space space 3 straight k with hat on top comma space space straight c with rightwards arrow on top space equals space straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top
therefore space space space space 2 space straight a with rightwards arrow on top minus straight b with rightwards arrow on top space plus space 3 straight c with rightwards arrow on top space equals space 2 left parenthesis straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top right parenthesis space minus space left parenthesis 2 straight i with hat on top space minus space straight j with hat on top space plus space 3 space straight k with hat on top right parenthesis space plus space 3 left parenthesis straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top right parenthesis
                             equals space 2 straight i with hat on top space plus space 2 straight j with hat on top space plus space 2 space straight k with hat on top space minus space 2 straight i with hat on top space plus space straight j with hat on top space minus space 3 straight k with hat on top space plus space space 3 straight i with hat on top space minus space 6 straight j with hat on top space plus space 3 straight k with hat on top space equals space 3 straight i with hat on top space minus space 3 straight j with hat on top space plus space 2 space straight k with hat on top
therefore space space space space open vertical bar space 2 straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space plus space 3 straight c with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 3 right parenthesis squared plus left parenthesis negative 3 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root space equals square root of 9 plus 9 plus 4 end root space equals space square root of 22 therefore space space space space unit space vector space parallel space to space 2 straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space plus space space 3 space straight c 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 equals space fraction numerator 2 straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space plus space 3 straight c with rightwards arrow on top over denominator open vertical bar 2 space close vertical bar end fraction space equals fraction numerator 1 over denominator square root of 22 end fraction left parenthesis 2 straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space plus space 3 space straight c with rightwards arrow on top right parenthesis 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 1 over denominator square root of 22 end fraction left parenthesis 3 space straight i with hat on top space minus space 3 space straight j with hat on top space space plus space 2 space straight k with hat on top right parenthesis space equals space fraction numerator 3 over denominator square root of 22 end fraction straight i with hat on top space minus space fraction numerator 3 over denominator square root of 22 end fraction straight j with hat on top space plus space fraction numerator 2 over denominator square root of 22 end fraction straight k with hat on top

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