How to find intersection point of lines p . . . x + 1 0 = y − 2 − 1 = z 1 and q . . . x − 1 − 1 = y + 6 3 = z + 6 4 ?

Question

How to find intersection point of lines  p  .  .  .            x      +      1        0    =            y      −      2              −      1        =      z    1   and   q  .  .  .            x      −      1              −      1        =            y      +      6        3    =            z      +      6        4   ?

Ada Harrington · Accepted Answer

Step 1Let             x      +      1        0    =            y      −      2              −      1        =      z    1    =  t  ∈      R   .Then   x  =  −  1  ,  y  =  2  −  t  ,  z  =  tSo, the parametric form of the first line is       c    1    (  t  )  =  (  −  1  ,  2  −  t  ,  t  )  ,     t  ∈      R   . If we do the same for the second line, we get it&#039;s parametric form      c    2    (  t  )  =  (  1  −  t  ,  3  t  −  6  ,  4  t  −  6  )  ,     t  ∈      R   . Thus,      c    1    (  t  )  =      c    2    (  t  )    ⟺    t  =  2.Consequently, the intersection point is   A  (  −  1  ,  0  ,  2  )

How to find intersection point of lines p . . . x + 1

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