7.7_bzat4e - the picture at right there is force F which is...

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Section 7.7 The Dot Product
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The Dot Product of Two Vectors
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Example If v=4i-2j and u=-2i+3j a. find v u b. find v v g g
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The Angle between Two Vectors
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Example Find the angle between v=2i-2j and w=-3i+5j. Round to the nearest tenth of a degree. θ -5 -4 -3 -2 -1 1 2 3 4 5 6 -5 -4 -3 -2 -1 1 2 3 4 5 x y
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Parallel and Orthogonal Vectors
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0 .0 0 Two vectors are parallel when the angle between them is 0 or 180 . Two vectors are orthogonal if the angle between them is 90 . We say the vectors are orthogonal not perpendicular.
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Example Are the following two vectors orthogonal? u=2i-4j v=6i+3j
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Projection of a Vector Onto Another Vector
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You know how to add two vectors to obtain a resultant vector. We now reverse this process to express a vector as the sum of two orthogonal vectors. By doing this you can determine how much force is appli 1 2 ed in a particular direction. As in
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Unformatted text preview: the picture at right there is force F which is pulling the boat down the ramp. F is the force pressing against the ramp. The resultant force F is gravity. Example If v=4i+3j and w=-3i+5j, find the projection of v onto w.-6-5-4-3-2-1 1 2 3 4 5 6 7-6-5-4-3-2-1 1 2 3 4 5 6 x y v w Work: An Application of the Dot Product Example 30 50 lbs An person pulls a sled with her dog on it along level ground by exerting a force of 50 pounds on a rope that makes an angle of 30 with the horizontal. How much work is done pulling the sled 100 feet? (a) (b) (c) (d) Find the angle between v and w. Round to the nearest tenth of a degree.v=i-j and w=2i+3j. 30 100.7 101.3 29.5 (a) (b) (c) (d) Find v (w+u) if v=i-j, w=2i+3j and u=-3i+j g 1 4 5---...
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7.7_bzat4e - the picture at right there is force F which is...

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