MHB How can we determine the intersection point of two lines with given equations?

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To determine the intersection point of the lines L1 and L2, first establish their parametric equations and equate them to find common coordinates. The lines are parallel if their direction vectors are scalar multiples; otherwise, they may be skew or intersecting. In this case, the direction vectors are not scalar multiples, indicating they could either intersect or be skew. By solving the system of equations derived from equating the parametric forms, it was confirmed that the lines intersect at the point (4, -1, -5). This solution aligns with the information provided in the book.
  • #31
Yep, now apply the methods of checking I mentioned above. (Nod)
 
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  • #32
im actually not getting the same answers. i think i made a mistake.
 
  • #33
t=2
 
  • #34
it does satisfy the third equation as well. so now i plug in s and t into the parametric equations and and get x,y,z which turns out to be (4,-1,-5) and i checked with the back of the book. it's right :)
 
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