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Paul
May 6, 2021

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### Section 1-1 : The 3-D Coordinate System

1. Give the projection of $$P = \left( { - 9,1,5} \right)$$ onto the three coordinate planes.
2. Give the projection of $$P = \left( {3, - 2, - 5} \right)$$ onto the three coordinate planes.
3. Which of the points $$P = \left( {8, - 9,3} \right)$$ and $$Q = \left( { - 6,4, - 5} \right)$$ is closest to the $$xz$$-plane?
4. Which of the points $$P = \left( {8, - 9,3} \right)$$ and $$Q = \left( { - 6,4, - 5} \right)$$ is closest to the $$xy$$-plane?
5. Which of the points $$P = \left( {5, - 4,3} \right)$$ and $$Q = \left( { - 6,3,9} \right)$$ is closest to the $$x$$-axis?
6. Which of the points $$P = \left( {5, - 4,3} \right)$$ and $$Q = \left( { - 6,3,9} \right)$$ is closest to the $$y$$-axis?

For problems 7 – 9 list all of the coordinates systems ($$\mathbb{R}$$, $${\mathbb{R}^2}$$, $${\mathbb{R}^3}$$) that the given equation will have a graph in. Do not sketch the graph.

1. $$8z + \frac{{x + 1}}{{{y^2} + 2}} = 4x$$
2. $$\sqrt {y + 2} = 6$$
3. $$\displaystyle 7{y^3} - \frac{2}{{x + 1}} = xy$$