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Unformatted text preview: Section 10.2: Vectors Collect homeworks, timesheets, diagnostic quizes, and summaries of section 10.3. Hand out diagnostic quiz handout to those who needs one Section 10.3: The dot product How many of you have seen the dot product before in two dimensions? How many of you have seen the dot product before in three dimensions? Main ideas? ..?.. • Algebraic and geometric formulations of the dot product • The relationship between the sign of a • b and the angle between a and b • Orthogonal vectors • Vector and scalar projections The dot product (aka inner product or scalar product) of two vectors is a scalar: Algebraic formulation: ..?.. 〈 a 1 , a 2 , a 3 〉•〈 b 1 , b 2 , b 3 〉 = a 1 b 1 + a 2 b 2 + a 3 b 3 Geometric formulation: ..?.. a • b =  a   b  cos θ where θ is the angle between the vectors a and b . Combining these two formulas, we get a way to compute the angle between two vectors (or at least its cosine): use the first formula to compute the dot product, and then plug...
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 Fall '11
 Staff
 Linear Algebra, Vectors, Dot Product, Inner product space

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