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At what times does the object intersect one of the coordinate planes?

  1. Sep 28, 2011 #1
    1. The problem statement, all variables and given/known data
    r(t)={sin(pi*t),ln(t),((1/4)e^t}

    At what time(s) does the object intersect one of the coordinate axes?

    At what time(s) does the object intersect one of the coordinate planes?

    During what times t is the object in the first octant?


    2. Relevant equations

    Not sure??

    3. The attempt at a solution

    I know points on the z-axis have the form (0,0,z). The curve will intersect the z-axis if x(t) and y(t) are both 0 at the same time (t value). Same for the x-axis and y-axis.

    Points in the yz-plane have the form (0,y,z), the x-coordinate of the point must be 0. So for this I need to find the values of t for which x(t)=0. Same for the xy- and xz-planes.

    I really am not sure how to start. Can anyone point me in the right direction?? Formula maybe?? Or show me an example done using a position vector?
     
    Last edited by a moderator: Sep 28, 2011
  2. jcsd
  3. Sep 28, 2011 #2

    Mark44

    Staff: Mentor

    Your reasoning is correct, so you have already made a good start. Your vector function r(t) lists x(t), y(t), and z(t). For the first problem you need to have sin(pi*t) = 0 and ln(t) = 0 for the same value of t.

    A point is in the first octant if all three coordinates are positive.
     
  4. Sep 28, 2011 #3
    sin(pi*t) = 0
    sooo sin(pi*t)=ln(t) , then solve for t?
    ln(t) = 0
     
  5. Sep 28, 2011 #4

    Mark44

    Staff: Mentor

    No, you don't just want the points at which sin(pi*t) = ln(t) - you want to solve the system of equations
    sin(pi*t) = 0
    ln(t) = 0
     
  6. Sep 28, 2011 #5
    Ohhh soo...
    [URL]http://www2.wolframalpha.com/Calculate/MSP/MSP118919ha265g6c4b58g80000500gabba95c6h992?MSPStoreType=image/gif&s=23&w=156&h=18[/URL]
    [URL]http://www2.wolframalpha.com/Calculate/MSP/MSP119419ha265g6c4b58g8000022fg02efc8adeba9?MSPStoreType=image/gif&s=23&w=500&h=22[/URL]

    so x and y are 0 when t = 1 and I have to do the same for the x and y axis because that was for the z axis?
     
    Last edited by a moderator: Apr 26, 2017
  7. Sep 28, 2011 #6
    any help on how to find when it intersects a plane??
     
  8. Sep 28, 2011 #7

    Mark44

    Staff: Mentor

    Your image links are bad.
    Yes.
     
    Last edited by a moderator: Apr 26, 2017
  9. Sep 28, 2011 #8

    Mark44

    Staff: Mentor

    Do what you described in post #1
     
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