Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

itzmashy

  • 2 years ago

a plane contains points p(4,0,0) q (0,5,0) and r(0,0,2) a - sketch the plane b - find a vector perpendicular to the plane

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

    I don't know about sketching it, but if you want a vector perpendicular to it you need to find two vectors, \(\vec u\) and \(\vec v\) that lie in the plane you can do that by finding the vectors between the various points with a common vertex

  2. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1337148180943:dw|so here are our three points if we can find\[\vec u=\overrightarrow{pq}=p-q\]and\[\vec v=\overrightarrow{qr}=r-q\]

  3. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1337148370560:dw|\[\vec u=p-q=\langle4,-5,0\rangle\]\[\vec v=r-q=\langle0,-5,2\rangle\]the cross product of these vectors will be normal to the plane

  4. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\vec n=\vec u\times\vec v\]

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

    |dw:1337148472550:dw|

  6. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah, that's a good graph :)

  7. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    all that stuff I said still works though

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

    wait.. \[pq = p-q?\] but then you have \[qr = r -q\] i'm confused here:(

  9. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    typo, my bad I sort of invented my own notation there on the left

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

    ohh okay so it's suppsoed to he pq = q-p, right?

  11. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you can do it many ways, but they need a common vertex the vector p-q points toward p from q the vector r-q points toward r from q so this should just be\[pq=p-q\]\[rq=r-q\]as in the distance from p and r to q, respectively

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

    so then \[u x v = (-4 x 0, -5 x 5, 2 x 0) = < 0, -10, 0> ?\]

  13. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no that's not how you take a cross product...

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

    oh wait.. so.. nope you lost me again lol i'm sorry..

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

    so you're picking one point as the middle point, and then creating two vectors from it?

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

    and then crossing them?

  17. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    exactly :)

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

    and if i'm finding a vector PR, then its r -p, right? second point, minus first point? o.O

  19. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I sort of am making up the notation... whether it is supposed to be written PR or RP I really don't know all that matters is that you're consistent in your choice of vertex

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

    so, pr = < -4, 0, 2> pq = <-4, 5, 0> pr x pq = <-16, 0, 0> ?!

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

    but when i'm finding any vector, like for example PR, then how would i find it? r - p, or p-r? just in general, not related to this problem

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

    so getting the cross product of two vectors on a plane, gets me a vector perpendicular to the plane?

  23. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let me check you on that cross product... as far as what minus what is concerned, in a-b the vector points toward a so it is vector=(to point)-(from point)

  24. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ...so if you want a vector that points from p to r you write r-p

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

    okay! perfect :D thank you!!! one more question?

  26. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sure :)

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

    find an equation of the plane containing points P Q and R

  28. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thankfully once you have the normal vector to the plane this is a piece of cake just put the numbers in the components of the normal vector as the coefficients

  29. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the normal vector\[\vec n=\langle P,Q,R\rangle\]implies the plane\[Px+Qy+Rz=d\]where \(d\) is some constant

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

    and the normal vector was (16, 0 , 0)? so its 16x + 0 + 0 = d?

  31. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh I didn't check, but that seems wrong...

  32. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hold on...

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

    i crossed it in incorrectly lol hold on

  34. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah I got <2,-20> on the first try, but I'm tired so let me try again

  35. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry <2,0,-20>

  36. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but wait that way still be wrong...

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

    really? pellet.. i got <10 8 20> =\

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

    whats your pq and pr? =\

  39. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let me try again\[\vec u\times\vec v=\left|\begin{matrix}\hat i&\hat j&\hat k\\-4&5&0\\-4&0&2\end{matrix}\right|\]

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

    this is what i got: (10-0)i - (-8-0)j +(0+20)k is that wrong? :(

  41. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\vec u\times\vec v=\left|\begin{matrix}\hat i&\hat j&\hat k\\-4&5&0\\-4&0&2\end{matrix}\right|=10\hat i+20\hat k-8\hat j\]ok now we agree :)

  42. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so that is\[\vec n\]

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

    but.. but.. i got 10i + 8j + 20k, doesn't the - distribute to the 8? :(

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

    or.. it doesnt??

  45. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    my bad told you I'm tired

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

    no worries!!! i totally understand hahha

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

    so then i think i'm supposed to plug in the variables and a point so.. 10(x-4)+8(y-0)+20(z-0)=0?

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

    10x +8y +20z =40?

  49. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, that's exactly what you do I know the method, I just can't execute it when I'm sleep deprived :P

  50. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    looks right though

  51. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ...of course you could have picked any point and you would have gotten the same d

  52. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and you can simplify it obviously too 5x +4y +10z =20

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

    so the vector perpendicular to the plane is < 10, 8, 20>, and the equation of the plane containing points p q and r is 10x+8y+20z = -40?

  54. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    isn't it positive? you said so yourself, and I agree

  55. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the 40 I mean

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

    oops yeah hehe :D thats what i wrote down!

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

    yayyyy!!!! i think i get it!!! thank you soooo much!!!!!!!!

  58. colorful
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    welcome, and g'night :)

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

    sleep well!~!!!!

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.