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r
and r2
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
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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