Question about parametization vs vector field.

[ozone]

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 F^ ⃗=xi ^⃗+(x+y) j ^⃗+(x-y+z)k^⃗ .

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!

 

[dikmikkel]

You can set up the cross product and substitute back in t in terms of x,y,z.

 

[ozone]

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