Vector components resolution

In summary, vector components are defined along mutually perpendicular axes, typically the x and y axes. However, as one learns more about vectors, they may also encounter axis rotations where the axes are replaced by other mutually perpendicular directions. The components of a vector are always along their respective axes, but the vector as a whole can point in any direction.
  • #1
MIA6
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What's the definition of "vector components"? I mean that when I resolve a vector into two components, my teacher taught us to find its x-component which is on x-axis and y-component on y-axis, so if it be the case, then this vector must not be on either x-axis or y-axis but between. So is that the components of a vector must be on x-axis and y-axis? Or it may depends, as long as the two components are perpendicular to each other, and the vector is between them, it's okay?
Hope you can tell me, thanks.
 
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  • #2
Vectors are defined with components along mutually perpendicular axes. In the most elementary 2-d case, these are the x and y axes. However as you learn more about it, you will learn about axis rotations, where the axes are replaced by other mutually perpendicular directions.
 
  • #3
MIA6 said:
I mean that when I resolve a vector into two components, my teacher taught us to find its x-component which is on x-axis and y-component on y-axis, so if it be the case, then this vector must not be on either x-axis or y-axis but between.
Why do you say that? Why can't a vector have an x or y component equal to zero?
So is that the components of a vector must be on x-axis and y-axis?
The components--by definition--are along their axes.
Or it may depends, as long as the two components are perpendicular to each other, and the vector is between them, it's okay?
The x and y components will always be perpendicular to each other--but the complete vector can point in any direction.
 

What is the meaning of "vector components resolution"?

Vector components resolution is a mathematical technique used to break down a vector into its horizontal and vertical components. This method is commonly used in physics and engineering to analyze the motion of an object in two dimensions.

Why is vector components resolution useful?

Vector components resolution allows us to simplify complex vector problems into simpler components, making it easier to solve and understand. It also helps us analyze the individual effects of each component on the overall vector.

How do you find the horizontal and vertical components of a vector?

To find the horizontal and vertical components of a vector, we use trigonometric functions such as sine, cosine, and tangent. The horizontal component is calculated by multiplying the magnitude of the vector by the cosine of the angle it makes with the horizontal axis. The vertical component is calculated by multiplying the magnitude of the vector by the sine of the angle it makes with the horizontal axis.

What is the relationship between the components and the original vector?

The components and the original vector are related by the Pythagorean theorem. The magnitude of the original vector is equal to the square root of the sum of the squares of its horizontal and vertical components. In other words, the original vector is the hypotenuse of a right triangle formed by its components.

Can vector components resolution be used for vectors in three dimensions?

Yes, vector components resolution can be extended to vectors in three dimensions. In this case, the vector is broken down into its components along the x, y, and z axes. The process is similar to finding the horizontal and vertical components, but now we use three-dimensional trigonometry to calculate the components.

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