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Help, Parametric and vector eqns of a lines

  1. Oct 23, 2004 #1
    well, im lost...im not sure if this goes in college or k-12, but im in grade 12 in canada...and im learning here, so i guess im at the right place,
    any wyas....i need help, with parametric and vector eqns of lines, since im failing this course horribly...my teacher sucks and marks hard and I dont get anything!...
    so now for the questions

    The angle ø, 0° < ø < 180°, That a line makes with the positive x-axis is called the angle of inclination of hte line.

    A) find the angel of inclination of each of hte following lines.
    _
    i) r = (2,-6) + t(3,-4) ii) r = (6,1) + t(5,1)

    B) prove that the tange of the angle of inclination is equal to the slope of hte line.
     
  2. jcsd
  3. Oct 23, 2004 #2

    robphy

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  4. Oct 23, 2004 #3
    that didnt help me even a remote bit...still lost....:(
     
  5. Oct 24, 2004 #4

    robphy

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    Plot r(t) on a graph (t along the horizontal axis, r along the vertical axis).
    Choose two values of t (say t=0 and t=1)
    Evaluate r at t=0. That gives you a point P with coordinates (t,r)=( 0, r(0) ).
    Evaluate r at t=1. That gives you a point Q with coordinates (t,r)=( 1, r(1) ).
    Calculate the slope of the line segment PQ.

    Now think of PQ as the hypotenuse of a right triangle,
    with one leg parallel to the horizontal t-axis
    and the other leg parallel to the vertical r-axis.
    The angle of inclination is an angle of that triangle.
    Use trigonometry to relate that angle to your triangle legs and the slope.
     
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