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Home / Calculus III / 3-Dimensional Space / The 3-D Coordinate System
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Section 6-1 : 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. \(\displaystyle 7{y^3} - \frac{2}{{x + 1}} = xy\)