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10.3 Dot Product (“multiplying vectors”)
Properties of the dot product Angle between two vectors using dot product
Direction CosinesProjection of a vector onto another vector
Work done by constant force
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The angle between two nonzero vectors with the same initial point is the smallest angle between them.
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Find the angle between the vectors v = <2, 1, -1> and w = <3, -4, 1>
Find the angle between the vectors v = <-2, 2, 1> and w = <2, 3, 6>
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Find the angle between the two vectors F1 and F2 where F1 = j-k and F2 = 2i-j+2k
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Find a number k such that u = <2, 3, 4> is orthogonal to v = <k, 3, -7>
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Find the direction cosines and angles of the vector v = (4, -2, -4)
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Normal Vector (orthogonal to PQ)
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Ex 2: Given a = <2, -6, 3> and b = <1, -2, -2>, find the vector projection of b onto a.
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Which of the following does not make sense?
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WORK: YOU HAVE TO CHANGE KINETIC ENERGY OF AN OBJECT TO DO WORK! IN OTHER WORDS: EXERTING FORCE DOES NOT EQUAL WORK!
Physics
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Application #1
A woman exerts a horizontal force of 25lb on a crate as she pushes it up a ramp that is 10 feet long and inclined at an angle of 20 degrees above the horizontal. Find the work done on the box.
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Applications in real life #2: work
W = (magnitude of force) (displacement)= |F||D|cos(theta)
A mass is dragged up an incline of 38 degrees for 2 m by a force of 5.8 N that is directed at an angle of 54 degrees to the horizontal as shown in the diagram. What is the work done?
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SEC. 10.3/ 1, 3, 9, 10, 11, 13, 15, 19, 21, 27, 31, 45, 69, 70
Homework/Classwork