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question mark

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

swapnali bordoloi , 13 Years ago
Grade
anser 1 Answers
APURV GOEL

Last Activity: 13 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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