What is the difference between components and coordinates of a vector?

The vector component is the product of the unit vector of an axis with its scalar component along this axis. A vector is the resultant of its vector components. Scalar components of a vector are differences of coordinates, where coordinates of the origin are subtracted from end point coordinates of a vector.

What are coordinates of a vector?

In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers that describes the vector in terms of a particular ordered basis. Coordinates are always specified relative to an ordered basis.

What are the components of coordinates?

The spherical coordinate system is commonly used in physics. It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r, polar angle θ (theta), and azimuthal angle φ (phi).

Is a vector the same as a coordinate?

A vector may be a coordinate (and the other way around) in which case there is no difference. A coordinate is always a vector but a vector is not always a coordinate. It is really a question of interpretation which depends on the context in which the vector or coordinate is being used.

Are vectors and coordinates the same?

When we express a vector in a coordinate system, we identify a vector with a list of numbers, called coordinates or components, that specify the geometry of the vector in terms of the coordinate system. Here we will discuss the standard Cartesian coordinate systems in the plane and in three-dimensional space.

What is the component method?

The component method of vector addition is the standard way to add vectors. If C = A + B, then: Cx = Ax + Bx. Cy = Ay + By.

Do coordinates depend on the basis of a vector?

They say that vector $F^n$ always has N components but coordinates depend on chosen basis and, therefore, it is meaningless to talk about coordinates when basis is unspecified. But don’t components depend on basis?

What is x vector component in Cartesian coordinate system?

Figure 2.16 Vector →A in a plane in the Cartesian coordinate system is the vector sum of its vector x- and y-components. The x-vector component →Ax is the orthogonal projection of vector →A onto the x-axis.

What are components of a vector?

Components are used to describe general vectors in a given vector space within a basis in terms of linear combinations. Components of a given vector also are coordinates in vector spaces, because univocally determine the position.

What is the direction of the Y-component vector → d?

The direction of the y -component is + ˆj, which is parallel to the direction of the + y -axis. Therefore, the y -component vector →Dy points up, as seen in Figure 2.17. The scalar y -component of vector →D is Dy = + 2.9. The displacement vector →D is the resultant of its two vector components.