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Unformatted text preview: (Section 6.4: Vectors and Dot Products) 6.28 SECTION 6.4: VECTORS AND DOT PRODUCTS Assume v 1 , v 2 , w 1 , and w 2 are real numbers. For now, we will deal with vectors in the plane. PART A: DOT PRODUCTS How do we multiply vectors? There are two common types of products of vectors: the dot product (also known as the Euclidean inner product ), and the cross product (also known as the vector product). Dot Product (Algebraic Definition) If v = v 1 , v 2 and w = w 1 , w 2 , then the dot product of v and w is given by: v • w = v 1 w 1 + v 2 w 2 In words, you add the products of corresponding components. Dot products, themselves, are scalars. Example 7,3 • 2, − 4 = 7 ( ) 2 ( ) + 3 ( ) − 4 ( ) = 14 − 12 = 2 PART B: PROPERTIES OF THE DOT PRODUCT See p.440 in Larson . All but Property #4 are shared by the operation of multiplication of real numbers. Property #1) The dot product is commutative: v • w = w • v Property #3) The dot product distributes over vector addition: a • b + c ( ) = a • b + a •...
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