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Vector Algebra

Question
CBSEENMA12034100
Wired Faculty App

Find the projection of the vector straight i with hat on top space minus space straight j with hat on top on the vector straight i with hat on top space plus space straight j with hat on top.

Solution

Let straight a with rightwards arrow on top space equals straight i with hat on top space minus space straight j with hat on top comma space space space space straight b with rightwards arrow on top space equals straight i with hat on top space plus space straight j with hat on top
 therefore space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals left parenthesis 1 right parenthesis thin space left parenthesis 1 right parenthesis space plus space left parenthesis negative 1 right parenthesis thin space left parenthesis 1 right parenthesis space equals 1 minus 1 space equals space 0 comma space space straight b space equals space square root of 1 plus 1 end root space equals space square root of 2
Projection of straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space equals fraction numerator straight a with rightwards arrow on top. space straight b with rightwards arrow on top over denominator straight b end fraction equals space fraction numerator 0 over denominator square root of 2 end fraction space equals 0.

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