Answer to Question #7693 in Calculus for swapnali

Question #7693
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
1
Expert's answer
2012-03-22T10:36:44-0400
Calculate dot product of these vectors in two ways:
1. using formula (r1,r2)=|r1|*|r2|*cos(r1,r2)=1*1*cos(a-b)
2. using coordinates:
since these vectors are radius-vectors and their end points are on the unit circle, coordinates of these vectors are following
r1={cos a,sin a}
r2={cos b,sin b}
So their dot product (r1,r2)=cos a*cos b+sin a*sin b
Therefore
cos(a-b)=cos a*cos b+sin a*sin b

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS