TABLE OF CONTENTS 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 product is equal to zero. In this chapter, this concept, which can be extended to matrices, will be explored to a greater extent. This chapter will also consider the transformation of coordinates which is often requisite to the conduct of a successful engineering analysis.
A vector in space may be described by its components which are projections in the three coordinate directions. In the Cartesian coordinate framework in Fig 6.1a, where unit vectors in the positive x, y and z coordinate directions are designated, respectively, by i, j and k, the vector P can be represented by
In a Cartesian coordinate system, the coordinate axes are mutually perpendicular and are said to be orthogonal. Any line segment from the origin to a point P(x, y, z) can be represented by a vector. For example, in Fig 6.1b, the three orthogonal axes are represented by x 1, x 2 and x 3. The line segment from the origin to the point P( x 1,
