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Help, Parametric and vector eqns of a lines

  • Thread starter saady87
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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.
 

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robphy
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that didnt help me even a remote bit...still lost....:(
 
  • #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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