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

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