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briteliner

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## Homework Statement

x1,x2) are the components of a 2 dimensional vector r when referred to cartesian axes along the directions i,j. derive the relations

x1'= cosΘ x1+sinΘ x2

x2'=-sinΘ x1+cosΘ x2

for the components (x1',x2') or r referred to new axes i',j' obtained by a rotation of the axes through an angle Θ about the k direction

## Homework Equations

## The Attempt at a Solution

i just wrote that r=x^2+y^2 which in this case would be x1^2+x2^2 and then accounted for rotation by multiplying by sin or cos theta and proving that x1^2+x2^2=x1'^2+x2'^2 but it don't think its sufficient