Chapter 12 - Vectors and the Geometry of Space - 12.4 Exercises - Page 839: 42

Maximum length of the vector $u \times v=15$ Minimum length of the vector $u \times v$$=0$

Length of the vector $u \times v= || u \times v||=|| u|| \times || v||| sin \theta|$ $u \times v= || u \times v||=|| u|| \times || v|| |sin \theta|= 5 \times 3 |sin \theta|=15 sin \theta$ Maximum of $|sin \theta|$=1 and minimum of $|sin \theta|$=0 Thus, Maximum length of the vector $u \times v=15 \times 1=15$ Minimum length of the vector $u \times v$$= 15 \times 0 =0$