Adding and Subtracting Vectors of Different Directions

In summary, to find the change in velocity given initial velocity of 6m/s[North] and final velocity of 3m/s[East], you would need to use vector addition by breaking down each vector into its x and y components and then subtracting the initial velocity from the final velocity. This method can be used even when the directions are not opposite.
  • #1
Balsam
226
8

Homework Statement


Given the initial velocity of 6m/s[North] and the final velocity of 3m/s[East], how would you find the change in velocity?

Homework Equations


Change in velocity= final velocity- inital velocity

The Attempt at a Solution


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I don't know how to do this. I know that if the directions were opposite, like north and south, I could make one direction negative and one positive and then subtract, and the sign infront of my answer would tell me the direction of my answer. But, I don't know what to do when the directions aren't opposites, like north and west or south and east. Is there a method for adding and subtracting vectors of different directions?
 
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  • #2
Yes. Googling vector addition should give you a pretty clear idea how to go about it.

Essentially, you break each vector into its x and y (and possibly z) components. But Google it for the specifics.
 

What are vectors and how do they differ from regular numbers?

Vectors are mathematical quantities that have both magnitude and direction. Unlike regular numbers, which only have magnitude, vectors have a specific direction associated with them. This direction can be represented by an arrow.

How do you add vectors of different directions?

To add vectors of different directions, you must first break them down into their respective components (x and y). Then, add the x-components together and the y-components together to get the resultant vector. The magnitude of the resultant vector can be found using the Pythagorean theorem.

Can vectors be subtracted?

Yes, vectors can be subtracted. To subtract one vector from another, you must first find the negative of the vector (flip the direction of the arrow). Then, follow the same steps as adding vectors by breaking them down into components and finding the resultant vector.

What is the difference between adding and subtracting vectors?

The main difference between adding and subtracting vectors is the direction of the resultant vector. When adding, the resultant vector will have the same direction as the original vectors being added. When subtracting, the resultant vector will have a different direction than the original vectors.

Why is it important to consider direction when adding and subtracting vectors?

Direction is important when adding and subtracting vectors because it affects the final outcome. Two vectors with the same magnitude but different directions can have very different resultant vectors. It is important to accurately represent the direction of a vector to ensure the correct calculation of the resultant vector.

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