Find tension as a vector on point A and point B

[bkw2694]

1. Homework Statement
The tension in the supporting cable AB is T = 425 N. Write this tension as a vector (a) as it acts on point A and (b) as it acts on point B. Assume θ = 30°. [***I've attached a picture of the exact problem]

The answer in my textbook says T_A = <221, -212, 294>
T_B = <-221, 212, -294>

Homework Equations

T^→ [/B]= (T)(n^→)

n^→ = (AB^→) / (||AB^→||)

The Attempt at a Solution

I started by finding the AB^→ which I used A = (0, 5cos(30), 5sin(30)) and B = (2, 0, 6), which gave me AB^→ = <2, -4.33, 3.5>.

Next I used n^→ = (AB^→) / (||AB^→||) to find n^→ = <.338, -.732, .5916>

Then I found T^→ = (T)(n^→) = <143.65, -311.1, 251.43>I'm not sure what I'm doing wrong here. The only thing I can think of is if I'm using incorrect points for point A

 

[Astronuc]

It looks like θ is in the x-y (azimuthal) plane, so it should not apply directly to the z-coordinate as one did for the coordinates of A, necessarily.

One needs to think in terms of two angles, poloidal and azimuthal. Note point B is offset from the polar axis.

 

[bkw2694]

It looks like θ is in the x-y (azimuthal) plane, so it should not apply directly to the z-coordinate as one did for the coordinates of A, necessarily.

One needs to think in terms of two angles, poloidal and azimuthal. Note point B is offset from the polar axis.

Thank you! I'm pretty sure fixed my problem. I absolutely hate when the textbook doesn't make it obvious which plane the angle is in.

So that changed my A to A = (-2.5, 4.33, 0), which changed my tension to the correct answer.