Minus sign in forces in space problem.

[masterflex]

minus sign in "forces in space" problem.

Homework Statement

see picture for problem.

Homework Equations

please see a picture (one is of problem, the other contains the relevant formula).

The Attempt at a Solution

I was able to solve the whole thing, then looked at the solution, and saw that I missed a minus sign (which changed some, but not all of my solutions). I just don't understand why that minus sign (denoted by red arrow) is necessary (besides giving you the right answer). Generally, how do you think through it to know you need one there? Thanks for you help.

 

[teknodude]

Can you post your solution to the problem? The solution you posted is probably from the solutions manual which is meant for instructors, so they skip a lot of steps. It doesn't even show a FBD, so obviously it's difficult to understand their solution.

 

[masterflex]

my work...

I've attached a picture of my work (where the minus sign confused me). And you can see that I get a different Theta_x.

My work:
theta_x = 75.5 degrees
theta_y = 30 degrees
theta_z = 64.3 degrees

solution book:
theta_x = 104.5 degrees
theta_y = 30 degrees
theta_z = 64.3 degrees

Also my force F (which is the force CD) has weird components that doesn't really reflect the correct direction. And I know it has to do with that minus sign that I'm struggling with (the minus sign that is pointed to by the red arrow in an earlier picture). I just can't make sense of that minus sign in a logical way.

Thank you.

 

[teknodude]

Look at how the coordinate system is defined in the problem. Which direction is the x-component of the tension CD pointing?

 

[masterflex]

that's it? awesome -- thanks a lot! It makes sense now.