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

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R7.3

Problem Statement[edit]

Find:

(a) The scalar product

(b) The magnitude of and .

(c) The angle between and .

For:

(1) for .

(2) for .

Solution (1)[edit]

(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)[edit]

(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