What are vector components?
It is how much of the vector is in each chosen direction.
Usually you chose component directions that are perpendicular to each other such as x, y, and z axes in your conventional coordinate system. Sometimes you might choose East, North and Up. This choice of directions perpendicular to each other prevents the components from influencing each other and is called "orthogonal" coordinates.
You need as many component directions as you have dimensions. For example on a plane, x and y (or east and north) will do.
Now the component of a vector in a direction along a coordinate is the magnitude of the vector times the cosine of the angle between the vector and the coordinate direction.
For example if you are headed 30 degrees north of east on a plane surface at 10 km/hr, that vector can be expressed by its "components" in the east and north directions.
The component in the East direction is:
10 cos(30 degrees) km/hr
The component in the north direction is:
10 cos(60 degrees) km/hr
i don't get it
Vector components refer to the individual parts or quantities that make up a vector. A vector is a mathematical entity that represents both magnitude and direction. It is commonly represented as an arrow pointing in a specific direction with a specific length.
To understand vector components, let's consider a two-dimensional Cartesian coordinate system. In this system, any vector can be broken down into two perpendicular components, typically referred to as the x-component and the y-component.
The x-component represents the magnitude of the vector in the horizontal direction (along the x-axis), while the y-component represents the magnitude in the vertical direction (along the y-axis). These components can be positive or negative, depending on the direction of the vector's arrow.
To determine the vector components, you can use trigonometry. If you have the magnitude of the vector (length of the arrow) and the angle it makes with the positive x-axis, you can calculate the x-component using the formula: x-component = magnitude * cos(angle).
Similarly, the y-component can be calculated using the formula: y-component = magnitude * sin(angle).
By breaking a vector down into its components, it becomes easier to perform calculations and understand how the vector affects different directions in a given coordinate system.