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Math Help - calc III help

  1. #1
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    calc III help

    Hello I'm new to this forum but in desperate need for some help so I thought I'd give it a try here.

    Your eye is at (4,0,0). You are looking at a triangular plate whose verticies are (1,0,1), (1,1,0), and (-2,2,2). The line segment from (1,0,0) to (0,2,2) goes through the plate. What portion of this line is hidden from view by the plate?

    ok so far I have found:
    -The equation of the plane that the plate is on which I got -3x+3y-3z-6=0
    -parametric equations of the line segment and got x=1-t, y=2t, and z=2t
    -then I plugged the parametric equation values for x,y, and z into the plane equation to solve for t to result in the values for x,y, and z of the point of intersection (of the plate and line segment) and got (-2,3,3)

    now from here I am lost on how to get the hidden part of the line segment. any help is appreciated
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  2. #2
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    I'll have to make the assumption that all of the line on one side of the plate IS visible, and all of the other side is NOT visible (so assuming the line doesn't 're-appear' from behind the plate).
    Then, figure out which end of the line segment is on the other side of the plate to you. It should be the one which is furthest from you, and also further from you than the plate-line intersection point is.
    Now, the length of line which is hidden by the plate will be the length of the line segment between the HIDDEN end of the segment and the plate-line intersection. Divide this length by the TOTAL length of the line segment, from end to end, and you should get some number between 0 and 1 (well, it WILL be between 0 and 1, otherwise something's broken). If this number is, say 0.56, then 56% of the line segment is hidden.

    But just be aware of that assumption I made at the start.
    BTW not entirely sure if this is calculus, someone might want to check.
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  3. #3
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    Quote Originally Posted by chug1 View Post
    I'll have to make the assumption that all of the line on one side of the plate IS visible, and all of the other side is NOT visible (so assuming the line doesn't 're-appear' from behind the plate).
    Then, figure out which end of the line segment is on the other side of the plate to you. It should be the one which is furthest from you, and also further from you than the plate-line intersection point is.
    Now, the length of line which is hidden by the plate will be the length of the line segment between the HIDDEN end of the segment and the plate-line intersection. Divide this length by the TOTAL length of the line segment, from end to end, and you should get some number between 0 and 1 (well, it WILL be between 0 and 1, otherwise something's broken). If this number is, say 0.56, then 56% of the line segment is hidden.

    But just be aware of that assumption I made at the start.
    BTW not entirely sure if this is calculus, someone might want to check.
    Thanks for the help. What I ended up doing was taking the intersection point I got and the end point (0,2,2) of the line segment and called it another line and found its length. Not entirely sure that's what was supposed to be calculated but thats what I did. ( I got frustrated with it so i just went with that)

    As far as might not being Calc 3 its for a college engineering based calc 3 class, however, the professor isn't the greatest in my book. He seems to give problems that make you think waaaay out of the box from the examples he gives and works out, some of which involve some understanding of physics even though its not a prerequisite for the class, but that's a whole different problem aside form the reason of this thread
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