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1.2: SCALARS AND VECTORS

By S. W. Anwane
From Fundamentals of Electromagnetic Fields

1.2 SCALARS AND VECTORS

As stated in the introduction, the term scalar refers to the class of quantities that can be represented by a single real number, either positive or negative. On the other hand, the term vector refers to the quantities that can be represented by a single real number, either positive or negative, along with direction. A general vector field A at origin of rectangular coordinate system may be resolved into three scalar components each parallel to three mutually perpendicular coordinate axes.


Here, A x , A y , A z are components along the x-, y-, and z-axis respectively Each may be a scalar function of (x, y, z) and a x, a y, a z are unit vectors along the x-, y-, and z-axes respectively. A unit vector is a vector of unit magnitude in the direction of the coordinate axes.

Position Vector: Let A ( x 1, y 1, z 1) be a point in space expressed in a three-dimensional Cartesian coordinate system formed by three mutually perpendicular x-, y-, and z-axes and a x, a y, a z are unit vectors along them. Then, the position vector of point A is the vector starting from origin O to the point A as shown in Fig. 1 1 and expressed as


OA=R A.


FIG. 1 1: Parallelogram...
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