Finding Angle in 3D using dot product

[KEØM]

Homework Statement

Shown are a mast and a portion of the rigging of a schooner. Members CD and EF lie in the same plane, and CD is of length 7.5 m and forms an angle of 45° with a vertical line drawn through C. Knowing that when $$\theta$$ = 45° the tension in rope BD is 250N, determine, (a) the angle between the rope BD and gaff CD, (b) the projection on CD of the force exerted by rope BD at point D.

Here is a link to a file sharing site with a picture of the problem. It is number 3.42 on the scanned page.

"[PLAIN problem3.42.pdf"]http://jumalafiles.info/showfile2-37705393236825434789501909625354498/problem342.pdf">download problem3.42.pdf[/URL]

Homework Equations

$$\vec{P}\bullet\vec{Q} = PQcos\theta$$

$$\vec{\lambda_{DC}}\bullet\vec{\lambda_{DB}} = cos\theta$$

where $$\vec{\lambda}$$ is a unit position vector defining the rope portion DB and member DC in the problem.

The Attempt at a Solution

I found $$\vec{\lambda_{DC}}$$ using the given angles but I cannot find $$\vec{\lambda_{DB}}$$ with the given info. Any thoughts?

Thanks in advance,

KEØM

 

[nvn]

KEØM or anyone in the forum: I have a question about angle theta. The location of point E and F is unknown. Therefore, from the information given, we cannot assume segment EF is horizontal. Since angle theta is measured from an axis parallel to the x-axis passing through point E, and is measured to segment EF (EF being generally not horizontal), then angle theta generally cannot be a horizontal angle. Therefore, how do we know the orientation of skew angle theta? What am I missing? Or is problem 3.42 poorly written?

 

[djeitnstine]

It is stated the the member CD makes an angle of 45 degrees with the vertical. So one can probably also assume that member EF makes a 45 degree angle with the vertical. However it does still seem poorly drawn.

It seems you can use T=250N along the entire rope to find DB

I will take a better look at it after class...

 

[KEØM]

I did not even think about that nvn. I did the problem assuming that it was horizontal. I now have the solution if you are interested.

It is the second problem in the file:

"[URL title="download file from Jumala Files"]http://jumalafiles.info/showfile2-94156951958121615508614376973722952/hw5_solution.doc [/URL]

 

[nvn]

Problem 3.41 and 3.42 are written wrong. Consequently, there are infinite correct solutions, depending on what one arbitrarily (illogically) assumes for the missing information in the problem statement.