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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

Find the component of vector space 3 straight i with hat on top minus 4 straight j with hat on top in direction of straight i with hat on top plus straight j with hat on top.


Dot product of two vectors is given by,

               straight A with rightwards arrow on top times straight B with rightwards arrow on top space equals space AB space cosθ

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#6 {main}</pre>

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#6 {main}</pre> in the direction of space straight B with rightwards arrow on top

        Acosθ straight B with hat on top space equals space fraction numerator straight A with rightwards arrow on top times straight B with rightwards arrow on top over denominator straight B end fraction straight B with hat on top

                   equals fraction numerator straight A with rightwards arrow on top times straight B with rightwards arrow on top over denominator straight B squared end fraction straight B with rightwards arrow on top

Given,

              straight A with rightwards arrow on top space equals space 3 straight i with hat on top minus 4 straight j with hat on top  and  straight B with rightwards arrow on top space equals straight i with hat on top plus straight j with hat on top

Thus,      

          straight A with rightwards arrow on top times straight B with rightwards arrow on top space equals space left parenthesis 3 straight i with hat on top minus 4 straight j with hat on top right parenthesis times left parenthesis straight i with hat on top plus straight j with hat on top right parenthesis space equals space 3 minus 4 space equals space minus 1

Magnitude of B,  open vertical bar 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 1 right parenthesis squared end root space equals space square root of 2

So, components of vector in the direction of  straight i with hat on top plus straight j with hat on top

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#6 {main}</pre> 

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