# Section 10.5 Overheads -...

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A line in space is completely determined by a point and a   vector parallel to the line . The  parametric equations  of the line passing through  ) , , ( 0 0 0 0 z y x P =   and parallel to  c b a v , , =  are  given by  tc z z tb y y ta x x + = + = + = 0 0 0 , , . Ex:   Write the parametric equations of the line through  P(3,-4,5) parallel to v = <-2,7,3>. Ex:   Write the parametric equations of the line passing  through the points  ) , , ( 7 5 3 1 = P and  ) , , ( 10 8 6 2 - = P . Two lines are  parallel  if and only if their corresponding  vectors are scalar multiples of each other.  If they are not  parallel, we can try  to find a point of intersection.

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If two lines are not parallel  and do not intersect  they’re  called  SKEW LINES . Ex:   Are the following lines parallel, intersecting, or skew  lines? L
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## Section 10.5 Overheads -...

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