University of Florida/Egm4313/s12.team8.dupre/R7.3

R7.3

Problem Statement

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Find:

(a) The scalar product  

(b) The magnitude of   and  .

(c) The angle between   and  .

For:

(1)   for  .

(2)   for  .

Solution (1)

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(a) We know that  

Plugging in our given   and   functions:

  (7.3.1)

Integrating (7.3.1) by parts where:

 

We find:

 

 

This leads us to the solution:

  where C=0.

(b) We know that the magnitude of a function is obtained as follows:

 

Plugging our given values in and using trigonometric identities:

  (7.3.3)

Using u substitution on (7.3.3) to integrate, where:

 

We find:

 

This leads to:

 

And allows us to solve for our answer:

 

Doing the same process (without needing to integrate by parts) for our given g function:

 

 

Giving us our final magnitude of:

 

(c) We know that:

 

Plugging in solved values shows:

 

Leading us to:

  

Solution (2)

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(a) We know that  

Plugging in our given   and   functions:

  (7.3.5)

Integrating (7.3.5), we find:

 

This leads us to the solution:

 

(b) We know that the magnitude of a function is obtained as follows:

 

Plugging our given values in and using trigonometric identities:

  (7.3.7)

This allows us to solve for our answer:

 

We now obtain the magnitude of the g function in the same way, as follows:

 

Which leads up to our final magnitude:

   

(c) We know that:

 

Plugging in (7.3.8) and (7.3.9) shows:

 

Leading us to:

  radians