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Chapter 6: Problem 87
What is a directed line segment?
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Help you prepare for the material covered in the first section of the next chapter. a. Does (4,-1) satisfy \(x+2 y=2 ?\) b. Does (4,-1) satisfy \(x-2 y=6 ?\)
Group members should research and present a report on unusual and interesting applications of vectors.
Use a graphing utility to graph \(r=\sin n \theta\) for \(n=1,2,3,4,5\) and \(6 .\) Use a separate viewing screen for each of the six graphs. What is the pattern for the number of loops that occur corresponding to each value of \(n ?\) What is happening to the shape of the graphs as \(n\) increases? For each graph, what is the smallest interval for \(\theta\) so that the graph is traced only once?
Let $$\mathbf{u}=-\mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \text { and } \quad \mathbf{w}=-5 \mathbf{j}$$ Find each specified scalar or vector. $$5 \mathbf{u} \cdot(3 \mathbf{v}-4 \mathbf{w})$$
Find the angle, in degrees, between \(\mathbf{v}\) and \(\mathbf{w}.\) $$\mathbf{v}=2 \cos \frac{4 \pi}{3} \mathbf{i}+2 \sin \frac{4 \pi}{3} \mathbf{j}, \quad \mathbf{w}=3 \cos \frac{3 \pi}{2} \mathbf{i}+3 \sin \frac{3 \pi}{2} \mathbf{j}$$
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