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ch2_9lecture - Todays Objective Students will be able to...

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DOT PRODUCT (Section 2.9) Today’s Objective : Students will be able to use the dot product to a) determine an angle between two vectors, and, b) determine the projection of a vector along a specified line. In-Class Activities : Check homework Reading quiz Applications / Relevance Dot product - Definition Angle determination Determining the projection Concept quiz Group problem solving Attention quiz
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APPLICATIONS For this geometry, can you determine angles between the pole and the cables?
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DEFINITION The dot product of vectors A and B is defined as A B = A B cos θ . Angle θ is the smallest angle between the two vectors and is always in a range of 0 º to 180 º . Dot Product Characteristics : 1. The result of the dot product is a scalar (a positive or negative number). 2. The units of the dot product will be the product of the units of the A and B vectors .
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DOT PRODUCT DEFINITON (continued) Examples: i j = 0 i i = 1 A • B = (A x i + A y j + A z k ) (B x i + B y j + B z k ) = A x B x + A y B y + A z B z
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