How to find resultant for 3 given vectors

In summary, the problem at hand is finding the resultant of three vectors A=(-4.0 m) on x-axis + (2.0 m) on y-axis, B= (6.0 m) on x-axis + (3.5 m) on y-axis, and C= (-5.5 m) on y-axis. The individual has tried drawing the vectors tip to tail, but is unsure how to find the resultant. Suggestions have been given to either use the component method or the geometry method, using the cosine and sine laws. It is also mentioned that the individual is a senior in physics and may need some assistance in the subject.
  • #1
idon'tgetit
1
0
We were given this problem over the weekend, but our teacher never explained how to do it and we have a quiz on vectors tomorrow and it may be on it. I tried, but couldn't get it...
- Find the resultant of the three vectors A=(-4.0 m) on x-axis + (2.0 m) on y-axis, B= (6.0 m) on x-axis + (3.5 m) on y-axis, and C= (-5.5 m) on y-axis.

I drew it out and drew the vectors tip to tail, but I have no idea a resultant can be made from three vectors. I was thinking maybe the component method, but that would be 6 triangles and it didn't seem right. Please help! :confused:
 
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  • #2
I am a senior in physics, so I'm not exactly an expert. But I have already completed that chapter. Simply add all of the Y's to find the y-component of Vr ([tex]V_ry[/tex]). Next, add all of the X's to find the X component of Vr ([tex]V_rx[/tex]). Then:
[tex]V_r = \sqrt{V_ry^2 + V_rx^2}[/tex]

Correct me please if I am mistaken (physics is giving me trouble).
 
  • #3
You find the resultant of three vectors the same way you find the resultant of two- you add them! Yes, you can draw them "tail to tip" and treat it as a geometry problem- although the geometry is a little complicated.

Probably the simplest way is to do what mlowrey said: convert each into x and y components, add the x-components, add the y-components.

If you are not comfortable with components and have only used "triangles" to add two vectors then you can do that also. Start with two of the vectors, draw them "tail to tip" and use the cosine law and sine law to find the resultant. Now take that resultant vector do exactly the same to add it to the third vector.
 

1. How do I find the resultant for 3 given vectors?

To find the resultant of 3 given vectors, you will need to use vector addition. This involves adding the components of each vector together to find the final resultant vector.

2. What is vector addition?

Vector addition is a mathematical operation used to combine two or more vectors into a single vector. It takes into account the direction and magnitude of each vector to determine the final resultant vector.

3. Can I use the Pythagorean theorem to find the resultant of 3 given vectors?

No, the Pythagorean theorem is only applicable when dealing with right triangles. In the case of finding the resultant of 3 given vectors, you will need to use vector addition and trigonometric functions to calculate the final resultant vector.

4. How do I use trigonometric functions to find the resultant of 3 given vectors?

Trigonometric functions, such as sine, cosine, and tangent, can be used to calculate the components of each vector and then add them together to find the resultant vector. It is important to pay attention to the direction of each vector to ensure correct calculations.

5. Are there any shortcuts or formulas to find the resultant of 3 given vectors?

Yes, there are several formulas that can be used to find the resultant of 3 given vectors, such as the parallelogram law or the triangle law. However, it is important to understand the concept of vector addition and how to use trigonometric functions to ensure accuracy in calculations.

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