A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Find the equation of a plane that contains the lines (x - 1)/6= y/8= (z + 2)/2 and (x + 1)/3= (y - 2)/4= z+ 5.

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

    \[\frac{x-1}{6}=\frac{y}{8}=\frac{z+2}{2}\] and \[\frac{x+1}{3}=\frac{y-2}{4}=z+5\] just to make it easier to look at

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

    the direction vector of the first line call it \[\vec{v}=(6,8,2)\] and the corresponding direction vector of the second line call it \[\vec{u}=(3,4,1)\]

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

    Now calculate the cross-product \[\vec{v}\times\vec{u}\] and to make calculations a little easier note the scalar value 2 is common to the components of \[\vec{v}\]

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

    on closer inspection those lines are parallel

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

    so form a vector from a point on the first line to a point on the second, the cross that vector with either of the direction vectors, that vector will be the normal vector for the plane that contains both lines, then just plug the components of your new vector , and a point from either line, into the standard equation for a plan and there you have it

  6. 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.