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Vector Algebra

Question
CBSEENMA12034054
Wired Faculty App

Find open parentheses straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top close parentheses. space space open parentheses 3 space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close parentheses when
    straight a 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 5 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight j with hat on top space minus space space 3 space straight k with hat on top

Solution

Here, 
                straight a 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 5 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top
therefore space space space straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top space equals space left parenthesis 2 space straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top right parenthesis space minus space left parenthesis straight i with hat on top space minus space 2 space straight j with hat on top space plus space 5 space straight k with hat on top right parenthesis space equals space straight i with hat on top space plus space 3 space straight j with hat on top space minus space 8 space straight k with hat on top
      3 straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space equals space left parenthesis 3 space straight i with hat on top space minus space 6 space straight j with hat on top space plus space 15 space straight k with hat on top right parenthesis space plus space left parenthesis 2 straight i with hat on top space plus space straight j with hat on top space minus space 3 space straight k with hat on top right parenthesis space equals space 5 space straight i with hat on top minus space 5 space straight j with hat on top space plus space 12 space straight k with hat on top
therefore space space space space left parenthesis straight b with rightwards arrow on top space minus space straight a with rightwards arrow on top right parenthesis. space space left parenthesis 3 space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top right parenthesis space equals space left parenthesis straight i with hat on top space plus space 3 space straight j with hat on top space minus space 8 space straight k with hat on top right parenthesis. space left parenthesis 5 straight i with hat on top space minus space 5 straight j with hat on top space plus space 12 space straight k with hat 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 space space space space space space space space space space space space space space space space space space space space space space equals space left parenthesis 1 right parenthesis thin space left parenthesis 5 right parenthesis space plus space left parenthesis 3 right parenthesis space left parenthesis negative 5 right parenthesis plus space left parenthesis negative 8 right parenthesis thin space left parenthesis 12 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 space space space space space space space space space space space space space space space space space space space space space space equals space 5 minus 15 minus 96 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 space space space space space space space space space space space space space equals space minus 106 space space space space space space space space space space space space space space space space space space space space

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