Vector Addition using coordinates

[jumbogala]

Homework Statement

You have a vector, labelled A, with the coordinates (2,1,1). Subtract vector B, coordinates (3,-1,4) from vector A.

Homework Equations

Take vector A, and flip vector B in the opposite direction. Line up vector B's tip to vector A's tail, and draw the new vector from tail to tip.

What I am unsure about are those 3 coordinates. I have only learned in class to use two coordinates. What does the third one mean?

The Attempt at a Solution

I'm guessing that one number is the x-component, and that one is the y-component. I have no idea what the third one would be, however. Also, I have no idea what order they are in!

 

[Kurdt]

The third number is the z-component. They are always written in the order (x, y, z). In this context they are called the components of the vector. To add vectors given their components, just add x-components, to give the resultant vector x-component, the y-components to give the resultant vector y-component... etc.

 

[baba89]

Hello, thank you for reaching out with your question. It appears that you are working with three-dimensional vectors, which require three coordinates to fully represent their direction and magnitude. In this case, the first coordinate (2) represents the x-component, the second coordinate (1) represents the y-component, and the third coordinate (1) represents the z-component.

To subtract vector B from vector A, you can use the method of vector addition by flipping vector B in the opposite direction and lining it up with vector A. The third coordinate (1) will still represent the z-component, but it will not affect the calculation as vector B will be flipped in the opposite direction. The order of the coordinates does not matter, as long as they are consistent for both vectors.

I hope this helps clarify your understanding of vector addition using coordinates. If you have any further questions, please don't hesitate to ask. Keep up the good work in your studies!