Adding vectors in this 3-D problem

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In summary, the conversation discusses a problem involving adding 3D vectors with the same magnitude. The final position of the vectors is represented as (M,-M,M), but the magnitude of the resultant vector is also asked for. The conversation suggests representing the resultant vector in <Magnitude,Direction> format and using the Pythagorean theorem to solve the problem.
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huehuephy
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Homework Statement
Hi! I'm having a problem trying to figure out a 3D vector physic question. Some help would be appreciated!
Relevant Equations
Three vectors all have the same magnitude. The symbol for the magnitude of each of these vectors is M. The first vector points in the positive x direction. The second vector points in the negative y direction. The third vector points in the positive z direction. These three vectors added together are equal to a fourth vector . What is the magnitude of the fourth vector?
I gathered that the final position of the vectors when added up would be (M,-M,M), but I'm not sure if this is correct.
 
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huehuephy said:
Homework Statement:: Hi! I'm having a problem trying to figure out a 3D vector physics question. Some help would be appreciated!
Relevant Equations:: Three vectors all have the same magnitude. The symbol for the magnitude of each of these vectors is M. The first vector points in the positive x direction. The second vector points in the negative y direction. The third vector points in the positive z direction. These three vectors added together are equal to a fourth vector . What is the magnitude of the fourth vector?

I gathered that the final position of the vectors when added up would be (M,-M,M), but I'm not sure if this is correct.
Yes, that is one way to represent the resultant vector. The problem asks you for the magnitude of the result of adding those components. Can you change the representation of the resultant vector sum into <Magnitude,Direction> format? (and you don't need to figure out the direction part of it for this problem)

It probably also helps to draw a sketch of adding those 3 vectors nose-to-tail...
 
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Are you familiar with the Pythagorean therom?
 
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1. How do you add vectors in a 3-D problem?

To add vectors in a 3-D problem, you first need to determine the x, y, and z components of each vector. Then, simply add the x components together, the y components together, and the z components together to get the final vector sum.

2. What is the importance of adding vectors in a 3-D problem?

Adding vectors in a 3-D problem is important because it allows us to accurately represent and calculate the magnitude and direction of a resulting force or displacement in three-dimensional space. This is crucial in many fields such as physics, engineering, and computer graphics.

3. Can vectors be added in any order in a 3-D problem?

Yes, vectors can be added in any order in a 3-D problem. This is because vector addition is commutative, meaning that changing the order of the vectors being added does not change the result.

4. What is the difference between adding vectors algebraically and graphically in a 3-D problem?

Adding vectors algebraically involves breaking down each vector into its x, y, and z components and then adding them together to get the final result. Graphically, vectors are represented as arrows with their magnitude and direction, and the resulting vector is found by placing the tail of one vector at the head of the other and drawing a line from the tail of the first vector to the head of the second vector.

5. Are there any special rules for adding vectors in a 3-D problem?

Yes, there are a few special rules for adding vectors in a 3-D problem. These include the parallelogram rule, where the resulting vector is found by drawing the diagonal of a parallelogram formed by the two vectors being added, and the triangle rule, where the resulting vector is found by drawing the third side of a triangle formed by the two vectors being added.

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