Adding Vectors (r, θ, φ) - A Step-by-Step Guide

  • Thread starter Philosophaie
  • Start date
  • Tags
    Vectors
In summary, to add two vectors with spherical coordinates, you can either transform them to rectangular coordinates and then add them, or use trigonometry to determine the length and angles of the third side of a triangle formed by the two vectors. The latter method can be more complicated due to the need to determine the angle between the two sides.
  • #1
Philosophaie
462
0
How do you add two vectors:

Code:
(r1, theta1, phi1) + (r2, theta2, phi2)

I know if you break them down into x, y, z components you get the right answer but how do you add these vectors.
 
Mathematics news on Phys.org
  • #2
As you said, transform them to rectangular coordinates (xyz-components), add them, and then transform back to spherical coordinates.
 
  • #3
If you mean "without using components" (i.e. the hard way) you use trigonometry.

Draw a line segment with one end at (0, 0, 0) in the direction given by theta1 and phi1 with length r1. At its tip, draw a second line segment in the direction given by theta2 and phi2 with length r2. Finally, draw the line segment from (0, 0, 0) to the tip of the second line segment. This forms a triangle in which you know the length of two sides and the angle between them so can use the sine and cosine laws to determine the length and angles of the third side. It is determining the angle between the two sides that is complicated.
 

1. What are vectors (r, θ, φ) and how are they used in science?

Vectors (r, θ, φ) are mathematical quantities that have both magnitude and direction. In science, they are often used to represent physical quantities such as velocity, force, and electric fields.

2. How do you add vectors (r, θ, φ) together?

To add vectors (r, θ, φ), you must first convert them into Cartesian coordinates (x, y, z). Then, you can add the corresponding components of the vectors to find the resulting vector in Cartesian form.

3. What is the significance of the angles θ and φ in vector addition?

The angles θ and φ represent the direction of the vector in relation to the x, y, and z axes. They are crucial in determining the final direction of the resultant vector after addition.

4. Can vectors (r, θ, φ) be subtracted from each other?

Yes, vectors (r, θ, φ) can be subtracted using the same method as addition. However, when subtracting, you must subtract the corresponding components of the vectors instead of adding them.

5. Is there a graphical way to visualize vector addition (r, θ, φ)?

Yes, you can use vector diagrams to visualize vector addition. The initial vectors (r, θ, φ) can be represented as arrows starting from the origin of a coordinate system. The resultant vector will be the sum of these arrows, starting from the origin and ending at the final point.

Similar threads

Replies
2
Views
1K
Replies
2
Views
611
Replies
3
Views
265
  • General Math
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
29
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
19K
Replies
4
Views
1K
Replies
1
Views
1K
  • Linear and Abstract Algebra
Replies
3
Views
297
  • Calculus and Beyond Homework Help
Replies
5
Views
186
Back
Top