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Vector Algebra

Question
CBSEENMA12034014
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Find the direction cosines of the vector straight i with hat on top space plus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top.

Solution

 Let      straight a with rightwards arrow on top space equals space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top
 therefore space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis 3 right parenthesis squared end root space equals space square root of 1 plus 4 plus 9 end root space equals space square root of 14 therefore space space space space space straight a with hat on top space equals space fraction numerator open vertical bar straight a with rightwards arrow on top close vertical bar 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 14 end fraction left parenthesis straight i with hat on top space plus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top right parenthesis space space space space space space space space space space space space equals space fraction numerator 1 over denominator square root of 14 end fraction straight i with hat on top space plus space fraction numerator 2 over denominator square root of 14 end fraction straight j with hat on top space plus space fraction numerator 3 over denominator square root of 14 end fraction straight k with hat on top therefore space space space direction space cosines space of space straight a with rightwards arrow on top space are space fraction numerator 1 over denominator square root of 14 end fraction comma space fraction numerator 2 over denominator square root of 14 end fraction comma space fraction numerator 3 over denominator square root of 14 end fraction.

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