ABSTRACT
Figure 1.1 Vector A along x-, y-, and z-axes.Vector A is given by A A i A j A kx y z= + + (1.1) Here, i j k , , are fundamental unit vectors in the x-, y-, and z-directions. The absolute value of this vector is A A A A Ax y z= = + + 2 2 2 (1.2) If we define a direction in cosine terms as (cos a, cos b, cos g) = (l, m, n) (1.3)it reads A Ax = cosa A Ay = cosb l m n2 2 2 1+ + = (1.4) A Az = cosg 1.3 Scalar and Vector ProductsA scalar product is the length of vector A multiplied by the length of the projection of vector B onto vector A , as displayed in Fig. 1.2. From Fig. 1.2, we get A B A B A B A Bx x y y z z◊ = + + (1.5) A B A B◊ = cosq (1.6)
where q is the angle between the vectors A and B . q
Figure 1.2 Scalar products. Note that i i j j ◊ = ◊ =1 (1.7) i j j i ◊ = ◊ =0 (1.8) A vector product is a vector together with size and direction. Size is the area of a rectangle made by the vectors A and B . Direction R is a thumb point when one turns finger from plane
A to B according to the right-hand rule, as shown in Fig. 1.3.
