A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

) The two vectors u<-1,2,3> and v = <-2,3,2> determine a plane in space. Mark each of the vectors below as "T" if the vector lies in the same plane as u and "F" if not.

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1. <3,0,0> 2. <6,-9,-6> 3. <-4,7,8> 4. <-3,4,1>

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    There are a couple of ways I can think of to solve this, what do you think might be some useful properties to use?

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    First i dont get what does that mean by saying " two vecotrs u<-1,2,3> and v=<-2,3,2> determine a plane in space Does that mean they are on the planes or just two position vectors that determine the two points on the plane

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh. It's saying that any two vectors that are linearly independent (not parallel) will define a plane.

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Or rather, that those two vectors are not parallel and therefore define a plane

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You can also picture the tips of those vectors as lying in the plane

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so they are not parallel but "in the plane"

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    right. They are parallel to the plane, but not parallel to each other.

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok,, i have thought of using cross product

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Good idea. What will that tell you?

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the normal vector of the plane

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    indeed. What does it mean to be normal to a plane?

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    any vectors parallel to the plane, but not necessarily in the plane, will have a 0 dot product with the the normal vector?

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    any vector parallel to the plane will be in the plane

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and yes, all the vectors in the plane are orthogonal to the normal vector of the plane (the dot product of the vector and the normal will be 0)

  16. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    why any vector parallel to the plane will be in the plane?

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry this is a new idea to me...i am kinda dumb right now

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok, since the plane is given by two vectors

  19. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it intersects the origin

  20. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    because vectors start at the origin, and end on the point specified with <x,y,z>

  21. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    all vectors are so?

  22. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, vectors are simply directions, not positions

  23. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So all the vectors in the plane will be orthogonal to the normal of the plane.

  24. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok got it :) thanks~~~~!!!

  25. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh i have one more question

  26. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  27. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the textbook i am using talks about displacement vector, which is defined by the difference of two points in space, and it does not go through the origin... so are there different kinds of vectors?

  28. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No, vectors can be moved around

  29. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    they have a magnitude and a direction, but not a position

  30. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    But there are not really different kinds of vectors (except when you're talking about vectors in different vector spaces)

  31. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh so you can always visualize a vector starting at the origin and points toward some direction,,,kk i think i get it now Thanks :)

  32. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yep =)

  33. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.