Vector Projections: Same Projection onto XY Plane?

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SUMMARY

The discussion centers on the concept of vector projections onto the XY plane, specifically examining three curves: a) <t, t², e^t>, b) <e^t, t², t>, and c) <t, t², cos(t)>. Participants confirm that projecting onto the XY plane involves setting the z-coordinate to zero. This leads to the conclusion that curves a) and b) share the same projection, while curve c) differs due to the cosine function affecting the z-coordinate.

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Which of the following curves have the same projection onto the xy plane?
a) <t, t^2, e^t>
b) <e^t, t^2, t>
c) <t, t^2, cost>
 
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Projecting onto the xy plane means setting z = 0 ?
 
I don't know, but that makes sense.
 

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