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Vector Algebra

Question
CBSEENMA12034179
Wired Faculty App

Find a unit vector perpendicular to vectors
3 straight i with hat on top space plus space 2 straight j with hat on top space minus space straight k with hat on top comma space space 2 straight i with hat on top space plus straight j with hat on top space plus 3 straight k with hat on top

Solution

Let straight a with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 2 straight j with hat on top space minus 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 plus space 3 space straight k with hat on top
therefore space space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 3 2 cell negative 1 end cell row 2 1 3 end table close vertical bar space equals straight i with hat on top space open vertical bar table row 2 cell negative 1 end cell row 1 3 end table close vertical bar space minus straight j with hat on top space open vertical bar table row 3 cell negative 1 end cell row 2 2 end table close vertical bar space plus space straight k with hat on top space open vertical bar table row 3 2 row 2 1 end table close vertical bar space space space space space space space space space space space space space space space space space space space equals space left parenthesis 6 plus 1 right parenthesis space straight i with hat on top space minus left parenthesis 9 plus 2 right parenthesis space straight j with hat on top space plus space left parenthesis 3 minus 4 right parenthesis space straight k with hat on top therefore space space space space space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space 7 space straight i with hat on top space minus space 11 space straight j with hat on top space minus space straight k with hat on top therefore space space space open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar space equals space square root of 49 plus 121 plus 1 end root space equals space square root of 171 therefore space space space space unit space vector space perp. space to space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space equals plus-or-minus fraction numerator straight a with rightwards arrow on top cross times straight b with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar end fraction equals space plus-or-minus space fraction numerator 1 over denominator square root of 171 end fraction left parenthesis 7 space straight i with hat on top space minus space 11 space straight j with hat on top space minus space straight k with hat on top right parenthesis space

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