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...