We are given a 3D force. We'll need various relations.

$\overline{){{\mathbf{\left(}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\alpha}}{\mathbf{\right)}}}^{{\mathbf{2}}}{\mathbf{+}}{{\mathbf{\left(}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\beta}}{\mathbf{\right)}}}^{{\mathbf{2}}}{\mathbf{+}}{{\mathbf{\left(}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\gamma}}{\mathbf{\right)}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{1}}}$

**Part A**

The x-component of force is:

$\overline{){{\mathbf{F}}}_{{\mathbf{x}}}{\mathbf{=}}{\mathbf{F}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\alpha}}}$

We're given the magnitude of force to be 90N and α = 64°

The bolt is subjected to the force F, which has components acting along the x, y, z axes as shown.

Part A

If the magnitude of F is 90 N , and α = 64° and γ = 41°, determine the magnitude of Fx component.

Part B

Determine the magnitude of F_{y }component.

Part C

Determine the magnitude of F_{z} component.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Vectors in 3D concept. If you need more Vectors in 3D practice, you can also practice Vectors in 3D practice problems.