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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.

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There really isn’t a lot to do with this problem. We know that the \(xy\)-plane is given by the equation \(z = 0\) and so the projection into the \(xy\)-plane for any point is simply found by setting the \(z\) coordinate to zero. We can find the projections for the other two coordinate planes in a similar fashion.

So, the projects are then,

\(xy\) – plane : \(\left( {3, - 4,0} \right)\)

\(xz\) – plane : \(\left( {3,0,6} \right)\)

\(yz\) – plane : \(\left( {0, - 4,6} \right)\)