Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Calcmathlete Group Title

VECTOR PROBLEM The cross product of the normal vectors to two planes is a vector that points in the direction of the line of intersection of the planes. Find a particular equation of the plane containing (-3, 6, 5) and normal to the line of intersection of the planes 3x + 5y + 4z = -13 and 6x - 2y + 7z = 8 Can someone guide me through it?

  • one year ago
  • one year ago

  • This Question is Closed
  1. Calcmathlete Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Since no one is responding, let me start with a simpler question. Would the cross product be a vector that is perpendicular to the line it is pointing towards? If so, it would be a bit simpler...

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

    Well finding the cross product is pretty simple. (3,5,4)x(6,-2,7)=(43,3,-36) This is the direction the line of intersection is pointing in. I'm just confused about what they mean by a plane that is normal to the line of intersection. Does the plane pass through the line? Is the normal perpendicular to the line?

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

    Here's a cute little graph I made, it might help :P Blue lines are normals to planes and red line is cross product.

    • one year ago
  4. Calcmathlete Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, a normal when talking about vectors is defined as a vector (or something else) that is perpendicular to what it is normal to.

    • one year ago
  5. BluFoot Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    OK I get it, the cross product will the normal of your new plane. So this is easy. Your new plane looks like: 43x+3y-36z=d Plug in your point (x,y,z) and solve for d!

    • one year ago
  6. Calcmathlete Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    OH! I get it now...I read the question incorrectly... -_- I thought it said that it pointed in the direction of the line, not the direction the line would be in...so now since the normal and plane have the same coefficients, and because the line of intersection and the vector are parallel, I can just plug in the point on the plane to finish the problem?

    • one year ago
  7. BluFoot Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yeah, exactly. You're basically looking for a plane that is normal to the other two planes, they're just making it overly complicated by talking about the line of intersection.

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

    Thank you!

    • one year ago
    • Attachments:

See more questions >>>

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.