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Question about parametization vs vector field.

  1. Jul 6, 2012 #1
    I thought i had a strong understanding of parameterizing curves and sketching vector fields. However when I was going through my practice test I came across this problem which I don't full grasp

    Let [itex] F^ ⃗=xi ^⃗+(x+y) j ^⃗+(x-y+z)k^⃗ . [/itex]

    a) Find a point at which F ⃗ is parallel to the line described by the parametric equations x=5+t,y=6-2t,z=7-3t.

    I believe I actually solved this problem. I pulled out the vector piece of the parameterized line <t,-2t,3t>
    then I set x = t, y = -3t, z = -t (making the i, j, and k components of our F equal the i, j, and k components of our parametric line)

    However when I got to the next part I was completely stumped.

    b) Find a point at which F ⃗ is perpendicular to the line described by the parametric equations x=5+t,y=6-2t,z=7-3t.

    I know that I could try to set up a cros product or I could try to set up a dot product which is equal to 0. However I run into problems since one curve is parameterized in terms of t and the other one is not. Furthermore I have no idea how to parameterize a vector field!
     
  2. jcsd
  3. Jul 6, 2012 #2
    You can set up the cross product and substitute back in t in terms of x,y,z.
     
  4. Jul 7, 2012 #3
    alright thank you.. seems easy enough

    edit:

    Your suggestion helped give me some confidence.. but it was the dot product after substitution which helped me to find a solution
     
    Last edited: Jul 7, 2012
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