Math 21a, Fall 2007
Problems A,B Week 2, Math 21a, Multivariable Calculus
GPS Problem
Course head: Oliver Knill
Office: SciCtr 434
Problem A: The global positioning system GPS uses the fact that a receiver can get the difference of distances to two satellites (each GPS satellite sends periodically signals which are triggered by an atomic clock. While the distance to each satellite is not known, the difference from the distances to two satellites can be determined from the time delay of the two signals. The receiver does not need an atomic clock). Given two satellites P=(2,0,0), Q=(0,0,0) in space. Identify the quadric, whose distance to P is by 1 larger than the distance to Q. How many GPS satellites does your GPS receiver have to 'see' in space so that it can determine the position?
Problem B: Find the surface whose points have the property that the distance to the x-axes is half the distance to the parametrized line r(t) = (1,0,0) + t (0,0,1)."

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Math21b | Math 21a | Fall 2007 | Department of Mathematics | Faculty of Art and Sciences | Harvard University