A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Calc. III Find an equation of a plane containing the line r = <-5,2,-5> + t<11,2,-1> which is parallel to the plane -1x+3y-5z=31 in which the coefficient of x is -1.

  • This Question is Closed
  1. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    anything parallel to -1x+3y-5z=31 will be in the form -1x+3y-5z=D where D is a constant

  2. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    `Find an equation of a plane containing the line r = <-5,2,-5> + t<11,2,-1>` so we know the point (x,y,z) = (-5,2,-5) is on the line and on this unknown plane

  3. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, we're also given the \(\vec n\) of the parallel plane

  4. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\vec n = \langle -1~,~3~,~-5\rangle\]

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

    Okay, so how do we put all the given information together to find the equation of the plane??

  6. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    at this point you just plug (x,y,z) = (-5,2,-5) into -1x+3y-5z=D to find D

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

    Found out the D = 26

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

    Scratch that D = 36

  9. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    side note: take the dot product of <11,2,-1> and the normal vector to the plane that Jhannybean wrote you should get a dot product of 0 which shows that the entire line is contained in the parallel plane

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

    So the final answer will be -1x+3y-5z-36 :) TYYY!!!!

  11. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    -1x+3y-5z-36 = 0 or -1x+3y-5z=36

  12. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh I see, your \(P_0 = (-5~,~2~,~-5)\) , cross checking whether your normal vector and position vector = 0, we'll know if theyre orthogonal to one another. Then with \(\vec n = \langle -1~,~3~,~-5\rangle \) and \(P_0 = (-5~,~ 2~,~-5)\) we can fidn the equation of a parallel plane by :\[a(x-x_0)+b(y-y_0)+c(z-z_0)=0\]

  13. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Thats how I would find it...

  14. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[-1(x-(-5)) +3(y-2)-5(z-(-5))=0\]\[-(x+5)+3(y-2)-5(z+5)=0\]\[-x-5 +3y-6-5z-25=0\]\[-x+3y-5z=25+6+5\]\[-x+3y-5z=36\]

  15. Jhannybean
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1444016189424:dw| So you'll have like a vector running in between planes...Haha

  16. 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.