Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1 What you’ll learn about Two-Dimensional Vectors Vector Operations Unit Vectors Direction Angles Applications of Vectors … and why These topics are important in many real-world applications, such as calculating the effect of the wind on an airplane’s path.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 2 Directed Line Segment
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Velocity and Speed The velocity of a moving object is a vector because velocity has both magnitude and direction. The magnitude of velocity is speed.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Writing Velocity as a Vector
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Calculating the Effects of Wind Velocity
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework Homework Assignment #17 Read Section 6.2 Page 511, Exercises: 1 – 57 (EOO)
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about The Dot Product Angle Between Vectors Projecting One Vector onto Another Work … and why Vectors are used extensively in mathematics and science applications such as determining the net effect of several forces acting on an object and computing the work done by a force acting on an object.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Properties of the Dot Product Let u, v, and w be vectors and let c be a scalar. 1. u·v=v·u 2. u·u=|u| ·u=0 4. u·(v+w)=u·v+u·w (u+v) ·w=u·w+v·w 5. (cu) ·v=u·(cv)=c(u·v)
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Orthogonal Vectors The vectors u and v are orthogonal if and only if u·v = 0.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding a Force to Overcome Gravitational Pull Suppose Rafaela is sitting on a sled on a 45º slope. If Rafaela and the sled have a combined weight of 140 lb, how much force must Juan apply to a rope tied to the sled to prevent its sliding down the hill?
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding the Work Done by a Constant Force Find the work done by a force F of 50 lb acting in the direction (2, 3) in moving an object five feet from (0, 0) to a point in the first quadrant along the line y = x.