Cartesian Vector Notation

Consider a vector A with its x and y components represented in terms of unit vectors, i and j. Here the unit vectors have dimensionless magnitude of one.

Since the magnitude of any vector component is always a positive quantity, represented by scalars, A can be expressed as a Cartesian vector.

Here, a right-handed, rectangle coordinate system is used. The right-hand thumb points toward the positive z-axis, and the fingers curl from the positive x-axis toward the positive y-axis.

A 3-dimensional vector can be represented in rectangular cartesian coordinates using i, j, and k unit vectors. The direction of these vectors are represented depending on the positive or negative axes.

A vector is represented as the vector sum of its individual components, and its magnitude is expressed as the positive square root of the sum of the squares of its components.

Vector algebra operations are simplified by representing vector in the Cartesian form. It separates its magnitude and direction along the axes using unit vector notation.