MAT-262 Lecture Notes - Lecture 4: Cross Product, Parallelepiped, Triple Product
Document Summary
Provide a generalization to each of the key terms listed in this section. When it comes to multiplying one vector by another vector, then there are actually 2 di erent types of vector multiplications. When it comes to the notation of determinants, the determinant of order 2 can be classi ed by the following: = (a)(d) (b)(c) = ad bc det(cid:18)1 2. Example b3 c3(cid:19) a2(cid:18)b1 c1 b3 c3(cid:19) + a3(cid:18)b1 c1 b2 c2(cid:19) det . = 1 ( 3) 2 ( 6) + 3 ( 3) = det j i k a1 a2 a3 b1 b3 b2. = (cid:18)a2 a3 b3(cid:19) i (cid:18)a1 a3 b3(cid:19) j +(cid:18)a1 a2 b2(cid:19) k b1 b2 b1. = [2(6) 3(5)]i [1(6) 3(4)]j + [1(5) 2(4)]k. = [12 15]i [6 12]j + [5 8]k. Proof that both a a = 0 and b b = 0 for any vector a or b while in v3. a = h1, 2, 3i.
