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Homework Help: Vector - find a

  1. Jan 26, 2010 #1
    1. Given that the two lines r1 and r2 intersect, find the value of a and hence determine the point of intersection.
    r1=i+9j-3k+landa(i+j-k)
    r2=4i+ak+mew(6i+5j+k)




    2. Relevant equations



    3. I'm a little lost with this one. Do I need to rewrite in parametric form and then cartesian form then compare i and j components. Then find values of mew and landa. Then use r1 and plug in landa value and solve for point of intersection?
     
  2. jcsd
  3. Jan 26, 2010 #2
    Using this technique I get a=-6
    and point of intersection is -52i-45j-12k

    Could somebody check this please?
     
  4. Jan 26, 2010 #3

    Mark44

    Staff: Mentor

    At a point of intersection, r1 = r2,
    so <1 + s, 9 + s, -3 -s> = <4 + 6t, 0 + 5t, a + t>
    (I have dispensed with "landa" (lambda) and "mew" (mu), and replaced them with s and t.)
    For two vectors to be equal, their corresponding components must be equal.

    The value I get for a is 78.
     
  5. Jan 27, 2010 #4
    yes thank you. I made a mistake in my layout. I have 78 now.
    and
    4i+ak-12(6i+5j+k)
    4i+78k-72i-60j-12k
    which gives -34i-30j+33k
     
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