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## 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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##### Topics of Interest

1.3 POLAR COORDINATE SYSTEM Using a two-dimensional Cartesian coordinate system, we represent a point, say, A( x 1, y 1) as shown in Fig. 1 6. To locate this point, one has to travel the distance x...

2.4 The Coordinate Systems Up to this point we have kept our discussion quite general and used graphical representations when manipulating vectors. From a mathematical point of view it is very...

Vectors and Scalars/Unit vectors/Scalar Componets and Vector Components/Vectorial Areas/Dot Product/Vector Fields and Scalar Fields/The Gradient Vector/Line Integrals/Divergence and the Divergence...

6.1 INTRODUCTION The concept of orthogonality was briefly introduced in Section 1.7 where it was stated that two vectors are orthogonal (possess the property of orthogonality) if their scalar or dot...

In This Chapter Vector Analysis Vector Derivatives The Scalar Laplacian The Vector Laplacian Integral Theorems Integral Transforms The Dirac Delta Function Special Functions A scalar physical...

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