X – Vector Analysis

Publisher Summary This chapter discusses the vectors in three-dimensional space. Vector analysis is a branch of mathematics that is especially adapted to the formulation of equations describing physical phenomena that take place in ordinary three-dimensional space. A right-handed Cartesian reference x, y, z is introduced. Denoting the unit vectors along the three axes by i, j, k, a point with coordinates x, y, z is represented by the location vector r = xi + yj + zk. Corresponding to two vectors a(al, a2, a3) and b(bl, b2, b3), a sum and a scalar product can be defined as a special case of the general definition. The magnitude a of the vector a is defined by a2= a21+a22+a23. In vector analysis, an outer product is determined by the parallelogram with the vectors a and b as sides. The projections of the vectors a and b on the xOy-plane are the vectors(al, a2, 0) and (bl, b2, 0). It Similar expressions hold for the two other coordinate planes.