Writing a linear combination of unit vectors in spherical coordinates

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‘components’ or ‘coordinates’ is made, implied or required. The vectors exist be written as a linear combination of these vectors, i.e. in the form a a1e1 a2e2 The unit vectors are called base vectors when used for this purpose. Unit Vectors We are familiar with the unit vectors in Cartesian coordinates, where x points in the x-direction and y points in the y-direction.

Here, we will first state the general definition of a unit vector, and then extend this definition into 2D polar coordinates and 3D spherical coordinates. 2D Cartesian Coordinates Consider a point (x, y). A spherical vector is another method for extending the concept of polar vectors into three dimensions.

It is akin to an arrow in the spherical coordinate system. A spherical vector is specified by a magnitude, an azimuth angle, and a zenith angle. The magnitude is usually represented as ρ.

Writing a linear combination of unit vectors in spherical coordinates
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