1. ## 3D Force System

Hello all. Im so thankfull to have found this site and hope some one can help me. I have exams coming up and am basically completely stuck on these 3D force systems for some reason I cannot get them through my head.

Would anyone be able to walk me through these problems?

2. Originally Posted by monkeybars
Hello all. Im so thankfull to have found this site and hope some one can help me. I have exams coming up and am basically completely stuck on these 3D force systems for some reason I cannot get them through my head.

Would anyone be able to walk me through these problems?

The direction of the force is

$\displaystyle \overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA} = (-4, -4, 2)$

The length of this vector is: $\displaystyle |(-4, -4, 2)| = \sqrt{16+16+4} = 6$

The length correspond with magnitude $\displaystyle F = 30 kN = k \cdot |(-4, -4, 2)|~\implies~ k = 5$ and therefore $\displaystyle \vec F = (-20, -20, 10)$

3. Thanks a lot!! Any ideas with the other 3?

4. Originally Posted by monkeybars
Thanks a lot!! Any ideas with the other 3?
to Q13:

Keep in mind that the x-axis has the direction vector (1,0,0). Then use the formula

$\displaystyle \cos(\alpha) = \frac{(-4,-4,2) \cdot (1,0,0)}{6 \cdot 1}$

to calculate the angle between $\displaystyle \vec F$ and the x-axis.

The other two angles are calculated similarly. (For your confirmation only: If I didn't make a mistake it is answer a))

5. Thank u earboth!!