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Section 12.1 : 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. \(\displaystyle 8z + \frac{{x + 1}}{{{y^2} + 2}} = 4x\)
2. \(\sqrt {y + 2} = 6\)
3. \(\displaystyle 7{y^3} - \frac{2}{{x + 1}} = xy\)