Representing Vectors: Calculating Force & Angle

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In summary, when representing a vector with x and y components, you can either write it in component form as 5Nx^ + 6Ny^ or in magnitude and angle form. The choice depends on what is most convenient for the problem at hand. Both notations are correct and it is important to follow your professor's instructions if they have a preference.
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FS98
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I recently had a test question where I had to calculate a force on a charged particles from two other charges particles. The answer ended up having an x and a y component. I realized I wasn’t quite sure how to represent that vector. Should I just have written it as something like 5Nx^ + 6Ny^, or should I have solved for the magnitude of the resultant vector and stated the angle that the resultant vector was pointing in?
 
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FS98 said:
Should I just have written it as something like 5Nx^ + 6Ny^, or should I have solved for the magnitude of the resultant vector and stated the angle that the resultant vector was pointing in?
That's two different ways of writing the same thing, so neither is wrong.

If your professor wants you reporting your result one way instead of the other, then of course you'll do it that way... but generally you choose whichever notation is most convenient for the problem at hand. The angle/magnitude form is usually easier to visualize; the component notation is often easier if you have to do more calculations with the vector.
 
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Related to Representing Vectors: Calculating Force & Angle

1. What is a vector and how is it represented?

A vector is a quantity that has both magnitude and direction. It is represented by an arrow, where the length of the arrow represents the magnitude and the direction of the arrow represents the direction of the vector.

2. How do you calculate the magnitude of a vector?

The magnitude of a vector can be calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the vector's components. Alternatively, you can use the magnitude formula, which is the square root of the dot product of the vector with itself.

3. What is force and how is it related to vectors?

Force is a physical quantity that describes the interaction between two objects. It is represented by a vector because it has both magnitude (measured in Newtons) and direction. The direction of the force vector is the direction in which the force is acting.

4. How can you calculate the angle between two vectors?

The angle between two vectors can be calculated using the dot product formula, where the angle is equal to the inverse cosine of the dot product of the two vectors divided by the product of their magnitudes. Alternatively, you can use the cross product formula, where the angle is equal to the inverse sine of the magnitude of the cross product of the two vectors divided by the product of their magnitudes.

5. How are vectors used in real-world applications?

Vectors are used in various fields such as physics, engineering, and navigation. They are used to represent and calculate forces, velocities, and directions in real-world situations. For example, vectors are used in satellite navigation systems to determine the location and direction of an object in space.

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