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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