Calculating Vector Magnitudes by Breaking Down Components

In summary, adding vectors involves breaking them down into their x and y components, finding the magnitudes of each component, and then using the Pythagorean theorem to determine the resultant magnitude. Simply adding the magnitudes of vectors will not give a meaningful result.
  • #1
SMS
9
0
How do you add two vector magnitudes and find x components?
 
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  • #2
The easiest way to add vectors is by component. You then find the magnitude of the resultant. You cannot simply add magnitudes and get a meaningful result.
 
  • #3
??

OK, V1= of 3.0 m/s and is directed along the +x-axis. V2=2.0 m/s. So V3 = V1+V2. Right.


I was never really shown how to add vectors.


Thanks.
 
  • #4
SMS said:
OK, V1= of 3.0 m/s and is directed along the +x-axis.

See how you posted a magnitude and a direction there?

You need to do that every time.

V2=2.0 m/s.

In what direction?
 
  • #6
to add vectors you have to break them down to their x and y components. ie let's say a vector has a magnitude of 'A' and an angle of 'K', you have to get the magnitude in the x and the magnitude in the y, so Ax=A cos (K) and Ay=A sin (K), now that you broke it down to Ax and Ay you can add it to other vector that you have broken down, just add the like parts like Bx+Ax and By+Ay the use the pathagorean theom to get the resultent magnitude (x^2+y^2=z^2) where z is the resultant magnitude.
 

Related to Calculating Vector Magnitudes by Breaking Down Components

1. What is the formula for adding vector magnitudes?

The formula for adding vector magnitudes is √(a² + b²), where a and b are the magnitudes of the two vectors being added.

2. How do I determine the direction of the resultant vector when adding vector magnitudes?

The direction of the resultant vector can be determined by using trigonometry and the tangent function. First, find the angle between the two vectors using the inverse tangent function (tan⁻¹). Then, add or subtract this angle from the direction of one of the vectors to determine the direction of the resultant vector.

3. Can vector magnitudes be negative?

No, vector magnitudes cannot be negative. They represent the size or length of a vector and are always positive values.

4. What is the difference between adding vector magnitudes and adding vectors algebraically?

When adding vector magnitudes, only the size or length of the vectors is considered. When adding vectors algebraically, both magnitude and direction are taken into account. The resulting vector from adding magnitudes will only have a magnitude, while the resulting vector from adding vectors algebraically will have both a magnitude and direction.

5. Can I add more than two vector magnitudes at once?

Yes, you can add more than two vector magnitudes at once. The same formula of √(a² + b²) can be applied for any number of vectors being added. You can also use the parallelogram method or the head-to-tail method to add multiple vectors graphically.

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