chapter 2-4

chapter 2-4 - DOT PRODUCT (Section 2.9) Today's Objective:...

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Lecture Notes for Section 2.9 1 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 READING QUIZ 1. The dot product of two vectors P and Q is defined as A) P Q cos θ B) P Q sin θ C) P Q tan θ D) P Q sec θ 2. The dot product of two vectors results in a _________ quantity. A) scalar B) vector C) complex D) zero P Q θ
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Lecture Notes for Section 2.9 2 APPLICATIONS For this geometry, can you determine angles between the pole and the cables? For force F at Point A, what component of it (F 1 ) acts along the pipe OA? What component (F 2 ) acts perpendicular to the pipe? 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 .
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chapter 2-4 - DOT PRODUCT (Section 2.9) Today's Objective:...

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