This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: (8/1/08) Math 20C. Lecture Examples. Section 12.4. The cross product There are two directions perpendicular to two nonzero and nonparallel vectors v and w in xyzspace. They are distinguished by using the righthand rule : A nonzero vector u perpendicular to v and w has the direction given by the righthand rule from v toward w if, when the fingers of a right hand curl from u toward v , as in Figure 1, the thumb points in the direction of u . FIGURE 1 FIGURE 2 The righthand rule is used in the definition of the cross product of two vectors. Definition 1 The cross product v w of nonzero and nonparallel vectors v and w in xyzspace is the vector perpendicular to v and w with direction determined by the righthand rule from v toward w and whose length is  v w  =  v  w  sin (1) where is the angle with < < between v and w . (Figure 2). If v or w is the zero vector or they are parallel, then v w is the zero vector. The cross product has the properties listed in the next theorem. Notice the minus sign in equation (2) . Theorem 1 For any vectors u , v , and w in xyzspace and any number , v w = w v (2) ( v ) w = v ( w ) = ( v w ) (3) u ( v + w ) = u v + u w (4) . Lecture notes to accompany Section 12.4 of Calculus, Early Transcendentals by Rogawski. 1 Math 20C. Lecture Examples. (8/1/08) Section 12.4, p. 2 Calculating cross products with determinants Cross products can be calculated using the notation of determinants from linear algebra....
View
Full
Document
This note was uploaded on 08/31/2011 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.
 Spring '08
 Helton
 Calculus, Vectors

Click to edit the document details