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r and r2 r are unit vectors in the x-y plane making angles a and b with the positive x-axis. By considering r1 . r2 r r , derive cos (a − b) = cos a cos b + sin a sin b


r


and r2


r


are unit vectors in the x-y plane making angles a and b with the positive


x-axis. By considering r1 . r2


r r


, derive


cos (a − b) = cos a cos b + sin a sin b


Grade:

1 Answers

APURV GOEL
39 Points
9 years ago

if we write vectors in component form we get

R1 = R1cosa^i + R1sina^j

R2 = R2cosb^i + R2sinb^j

now taking dot product R1.R2 = (R1cosa^i + R1sina^j) . (R2cosb^i + R2sinb^j)

which is also equal to R1R2cos(a-b)

so we have R1R2cos(a-b) = (R1cosa^i + R1sina^j) . (R2cosb^i + R2sinb^j)

or cos (a − b) = cos a cos b + sin a sin b


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