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Chapter 6: Problem 46
The rectangular coordinates of a point are given. Find polar coordinates of each point. Express \(\theta\) in radians. $$(-1,-\sqrt{3})$$
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The components of \(\mathbf{v}=240 \mathbf{i}+300 \mathbf{j}\) represent the respective number of gallons of regular and premium gas sold at a station. The components of \(\mathbf{w}=2.90 \mathbf{i}+3.07 \mathbf{j}\) represent the respective prices per gallon for each kind of gas. Find \(\mathbf{v} \cdot \mathbf{w}\) and describe what the answer means in practical terms.
Using words and no symbols, describe how to find the \(\mathrm{d}\) product of two vectors with the alternative formula $$\mathbf{v} \cdot \mathbf{w}=\|\mathbf{v}\|\|\mathbf{w}\| \cos \theta$$
How do you determine if two vectors are orthogonal?
Graph the spiral \(r=\theta .\) Use a [-48,48,6] by [-30,30,6] viewing rectangle. Let \(\theta \min =0\) and \(\theta \max =2 \pi,\) then \(\theta \min =0\) and \(\theta \max =4 \pi,\) and finally \(\theta \min =0\) and \(\theta \max =8 \pi\)
Determine whether v and w are parallel, orthogonal, or neither. $$\mathbf{v}=-2 \mathbf{i}+3 \mathbf{j}, \quad \mathbf{w}=-6 \mathbf{i}-9 \mathbf{j}$$
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