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Section 12.1 : The 3-D Coordinate System

  1. Give the projection of \(P = \left( {3, - 4,6} \right)\) onto the three coordinate planes. Solution
  2. Which of the points \(P = \left( {4, - 2,6} \right)\) and \(Q = \left( { - 6, - 3,2} \right)\) is closest to the \(yz\)-plane? Solution
  3. Which of the points \(P = \left( { - 1,4, - 7} \right)\) and \(Q = \left( {6, - 1,5} \right)\) is closest to the \(z\)-axis? Solution

For problems 4 & 5 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. \(7{x^2} - 9{y^3} = 3x + 1\) Solution
  2. \({x^3} + \sqrt {{y^2} + 1} - 6z = 2\) Solution