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Vector Algebra

Question
CBSEENMA12033995
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For given vectors, straight a 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 2 space straight k with hat on top space and space straight b with rightwards arrow on top space equals space minus straight i with hat on top space plus space straight j with hat on top space minus space straight k with hat on top comma space find the unit vector in the direction of the vector straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top.

Solution

Here straight a 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 2 space straight k with hat on top comma space space space space straight b with rightwards arrow on top space equals space minus straight i with hat on top space plus space straight j with hat on top space space minus space straight k with hat on top
therefore space space space space space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space equals space straight i with hat on top space plus space straight k with hat on top
                 open vertical bar straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 1 right parenthesis squared plus left parenthesis 0 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space square root of 1 plus 0 plus 1 end root space equals space square root of 2
therefore space space space unit space vector space in space the space direction space of space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top
                             equals space fraction numerator straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close vertical bar end fraction space equals space fraction numerator 1 over denominator square root of 2 end fraction left parenthesis straight i with hat on top space plus space straight k with hat on top right parenthesis space equals space fraction numerator 1 over denominator square root of 2 end fraction straight i with hat on top space plus space fraction numerator 1 over denominator square root of 2 end fraction straight k with hat on top

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