Find the projection of  in the direction of . from Mathemati

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 Multiple Choice QuestionsShort Answer Type

171. For any two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top comma we always have open vertical bar straight a with rightwards arrow on top. space straight b with rightwards arrow on top close vertical bar space less or equal than space open vertical bar straight a with rightwards arrow on top close vertical bar space open vertical bar straight b with rightwards arrow on top close vertical bar.
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172. For any two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top, we always have open vertical bar straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar space less or equal than space open vertical bar straight a with rightwards arrow on top close vertical bar space plus space open vertical bar straight b with rightwards arrow on top close vertical bar
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173.

If straight a with rightwards arrow on top is any vector, then show that
         straight a with rightwards arrow on top space equals space left parenthesis straight a with rightwards arrow on top space minus space straight i with hat on top right parenthesis space straight i with hat on top space plus space left parenthesis straight a with rightwards arrow on top. space straight j with hat on top right parenthesis space straight j with hat on top space plus space left parenthesis straight a with rightwards arrow on top space. space straight k with hat on top right parenthesis space straight k with hat on top.

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174.

If straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top comma space 2 space straight i with hat on top plus 5 space straight j with hat on top comma space space 3 space straight i with hat on top space plus space 2 space straight j with hat on top space minus space 3 space straight k with hat on top space space and space straight i with hat on top space minus space 6 space straight j with hat on top space minus space straight k with hat on top, respectively, are the position vectors of points A, B, C and D, then find the angle between the straight lines AB and CD. Deduce that AB and CD are parallel.

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175. Find the projection of the vector straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 3 straight j with hat on top space plus space 2 straight k with hat on top on the vector straight b with rightwards arrow on top space equals straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight k with hat on top.
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176.

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.

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177.

Find the projection of the vector straight i with hat on top space plus space 3 space straight j with hat on top space plus space 7 space straight k with hat on top on the vector 7 space straight i with hat on top space minus space straight j with hat on top space plus space 8 space straight k with hat on top.

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178.

Find the projection of 8 space straight i with hat on top space plus space straight j with hat on top in the direction of straight i with hat on top space plus space 2 space straight j with hat on top space minus space 2 space straight k with hat on top.

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179.

Find the projection of straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top in the direction of straight i with hat on top space plus space straight j with hat on top.


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

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180.

Find the projection of straight b with rightwards arrow on top plus straight c with rightwards arrow on top on straight a with rightwards arrow on top where
         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 straight k with hat on top comma space space straight b with rightwards arrow on top space equals straight i with hat on top space plus space 3 space straight j with hat on top space plus space straight k with hat on top space and space straight c with rightwards arrow on top space equals space straight i with hat on top space plus space straight k with hat on top.

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