Vector Question: 3 dimensions inside a rectangular soild?

[zeion]

Vector Question: 3 dimensions inside a rectangular soild??

Homework Statement

Three forces of 5 N, 8 N, and 10 N act from the corner of a rectangular solid
along its three edges.
a. Calculate the magnitude of the equilibrant of these three forces.
b. Determine the angle that the equilibrant makes with each of the three
forces

Homework Equations

The Attempt at a Solution

I was able to solve a. by taking two vectors then using the resultant of those 2 with the third to calculate the equilibrant. But how can I know the angle with respect to each original vector? I'm not sure how to relate the angles if they are calculated on different planes

 

[Dick]

Homework Statement

Three forces of 5 N, 8 N, and 10 N act from the corner of a rectangular solid
along its three edges.
a. Calculate the magnitude of the equilibrant of these three forces.
b. Determine the angle that the equilibrant makes with each of the three
forces

Homework Equations

The Attempt at a Solution

I was able to solve a. by taking two vectors then using the resultant of those 2 with the third to calculate the equilibrant. But how can I know the angle with respect to each original vector? I'm not sure how to relate the angles if they are calculated on different planes

I would try writing down explicit vectors and using the dot product.

 

[zeion]

This chapter in the textbook doesn't talk about dot products though.

 

[Dick]

This chapter in the textbook doesn't talk about dot products though.

Then you'll have to use trig. The resultant vector makes a right triangle with each of the three forces. The length of the resultant is the hypotenuse and the force is a leg. And the angle is between them is what you want.

 

[zeion]

But then I only have 2 sides and no angles?

 

[Dick]

But then I only have 2 sides and no angles?

You have a right angle. The difference between the resultant and the forces is perpendicular to the force. Draw a picture with only two perpendicular forces.