Find the magnitude and the angle that it makes with the positive x-axis?

In summary, the problem asks to find the magnitude and angle of a vector in relation to the positive x-axis. The solution involves multiplying the vector by different components and adding them together, using the Pythagorean theorem to find the magnitude, and taking the inverse cosine of the x component divided by the magnitude to find the angle. The solution of F=179.37 at an angle of 91 degrees is confirmed by the conversation.
  • #1
shemer77
97
0

Homework Statement


find the magnitude and the angle that it makes with the positive x-axis?
http://imageshack.us/photo/my-images/594/unledzmo.png/


Homework Equations





The Attempt at a Solution


The answer that I have is
F= 179.37 at an angle of 91 degrees. Am I right?
I took F1 and multiplied that by <cos60,sin60>, F2 multiplied that by <cos135,sin135>,F3 multiplied by <cos270,sin270> and then I added up all those vectors. then I used the Pythagorean theorem to get the magnitude then I took the inverse cosign of the x component of the resulting vector divided by the magnitude to get 91 degrees.
 
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  • #2
That's what I got too. Good work!
 

1. What is the meaning of "magnitude" and "angle" in this context?

The magnitude refers to the size or length of the vector, while the angle represents the direction of the vector in relation to the positive x-axis.

2. How do you find the magnitude and angle of a vector?

To find the magnitude of a vector, you can use the Pythagorean theorem, which states that the magnitude is equal to the square root of the sum of the squares of the components of the vector. To find the angle, you can use trigonometric functions such as sine, cosine, and tangent.

3. What units are used to measure the magnitude and angle?

The magnitude of a vector is typically measured in units such as meters, kilometers, or feet, depending on the context. The angle is typically measured in degrees or radians.

4. How does the direction of the vector affect its magnitude and angle?

The direction of the vector will affect both the magnitude and angle. If the vector is pointing in the same direction as the positive x-axis, the angle would be 0 degrees and the magnitude would be equal to the x-component of the vector. If the vector is pointing in the opposite direction, the angle would be 180 degrees and the magnitude would be equal to the negative of the x-component.

5. Can the magnitude and angle of a vector be negative?

Yes, the magnitude and angle of a vector can be negative. A negative magnitude would indicate that the vector is pointing in the opposite direction of the positive x-axis, while a negative angle would indicate that the vector is pointing in the opposite direction of the positive y-axis.

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