EPF Lecture Notes for Section 2_9

EPF Lecture Notes for Section 2_9 - DOT PRODUCT Todays...

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DOT PRODUCT Today’s Objective : Students will be able to use the vector dot product to: a) determine an angle between two vectors, and, b) determine the projection of a vector along a specified line.
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APPLICATIONS If the design for the cable placements required specific angles between the cables, how would you check this installation to make sure the angles were correct?
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APPLICATIONS For the force F being applied to the wrench at Point A, what component of it actually helps turn the bolt (i.e., the force component acting perpendicular to the pipe)?
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DEFINITION Difficulties working in 3 dimensions 1. Find the angle between two lines 2. Find the components of force parallel to a line 3. Find the components of force perpendicular to a line What is the Dot Product? The Dot Product is the product of the magnitudes of A and B and the cosine of the angle between their tails
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DEFINITION The dot product of vectors A and B is defined as A B = AB cos θ . The 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: By definition, 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 ( i i ) + A x B y ( i j ) + A
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This note was uploaded on 05/06/2011 for the course MECHENG 201 taught by Professor Rankin during the Spring '11 term at Wisconsin Milwaukee.

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EPF Lecture Notes for Section 2_9 - DOT PRODUCT Todays...

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