John Taylor Classical Mechanics Chapter 1 Problem 22

[karmonkey98k]

Homework Statement

The two vectors a and b lie in the xy plane and make angles (alpha and beta) with the x axis. a. by evaluating a dot b in two ways prove the well known trig identity cos(alpha-beta)=cosalphacosbeta +sinalphasinbeta

Homework Equations

adotb=abcostheta=axbx+ayby

The Attempt at a Solution

Could not really come to the proper set-up.

 

[ehild]

Homework Statement

The two vectors a and b lie in the xy plane and make angles (alpha and beta) with the x axis. a. by evaluating a dot b in two ways prove the well known trig identity cos(alpha-beta)=cosalphacosbeta +sinalphasinbeta

Homework Equations

adotb=abcostheta=axbx+ayby

The Attempt at a Solution

Could not really come to the proper set-up.

How are the x,y components of a vector related to the angle they make with the x axis?

ehild

 

[karmonkey98k]

the angle they make is in the problem; the cos of the difference of the angles equals that result. i just cud not go from the dot product to that.

 

[tiny-tim]

hi karmonkey98k!

start with a = |a|cosαi + |a|sinαj