A community for students.
Here's the question you clicked on:
 0 viewing
 2 years ago
Do the points A(2,1,5), b(1,1,10), and c(8,5,5) define a plane? Explain why or why not.
 2 years ago
Do the points A(2,1,5), b(1,1,10), and c(8,5,5) define a plane? Explain why or why not.

This Question is Closed

phi
 2 years ago
Best ResponseYou've already chosen the best response.1use elimination to find if the three points are independent (not collinear)

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Elimination? I think no, because there is no position vector or a direction vector.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0@Phi What is elimination?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry if I sound persistent, but I still don't understand (I have looked through the link).

phi
 2 years ago
Best ResponseYou've already chosen the best response.1what kind of math are you studying?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Vectors, of Vectors and Calculus.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Specifically, Lines and Planes.

phi
 2 years ago
Best ResponseYou've already chosen the best response.1Do they teach you about independent vectors? How to tell if two vectors are independent?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I had difficulties understanding the course. I don't exactly know.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0equations of lines is the lesson (specifically)

phi
 2 years ago
Best ResponseYou've already chosen the best response.1or maybe more simple: find the equation of a line through 2 of the points, and show the 3rd point does not satisfy the equation. So you know all 3 points do not lie on the same line, and therefore define a plane.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0What's an equation of a line?

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I'm just looking thru my textbook here, but I can only see equation of a plane. I'll use Google now though.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0y=mx+b? How does that work for a 3space point?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1I think you do A + n(BA) e.g. (2,1,5)+n ((1,1,10)(2,1,5)) where n is any value (a scalar)

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0You mean like a vector equation? [x,y,z]=[xo,y0,zo]+t[a1,a2,a3]+s[b1,b2,b3]

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0But that wouldn't make sense to me...Aren't the ones with scalar multipliers direction vectors?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1BA points in the direction from A to B dw:1333072072947:dw you scale it to move along it. Add A so the direction vector starts at A rather than the origin so A+ n(BA)

phi
 2 years ago
Best ResponseYou've already chosen the best response.1*should be BA as the label

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. Maybe I should ask what I should actually do for this question then. I don't seem to be able to comprehend our conversation.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I just solve for that? All I had to do was plug them in at random onto a vector equation? Sorry, my eyes are starting to hurt.

phi
 2 years ago
Best ResponseYou've already chosen the best response.1It looks like the 3 points are not collinear, so they define a plane

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Wait, how do I determine collinear? And, do I just do as what I suggested 2 comments above?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1See if this helps http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfLines.aspx

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0How far should I read into this?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1Start at the paragraph below the ellipse.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. I just figured out that the equation of the line is the same as the vector equation.

phi
 2 years ago
Best ResponseYou've already chosen the best response.1Here is the equation of the line through points (2,1,5) and (1,1,10) (2,1,5) + n( 1 2, 11, 105) (2,1,5) +n( 3, 2, 5) Is there an n that gets us to the point (8,5,5)? n= 2 gives us (2,1,5)2(3,2,5) = (2+6, 1+4,510)= (8,5,5) so it looks like there are all on the same line.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0( 1 2, 11, 105) I'm confused about that. I was never taught to do that in class. Also, "Is there an n that gets us to the point (8,5,5)? n= 2 gives us (2,1,5)2(3,2,5) = (2+6, 1+4,510)= (8,5,5)" Do I figure out n's value by guess and check?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1No you don't guess. you have 3 separate equations for x,y,z example 2+n(3) = 8 is the first one. It requires n= 2. it turns out all of the equations work for 2. so point (8,5,5) is on the line

phi
 2 years ago
Best ResponseYou've already chosen the best response.1that is point (1,1,10)  (2,1,5) rewritten as ( 1 2, 11, 105)

phi
 2 years ago
Best ResponseYou've already chosen the best response.1Look at Example 1 in Paul's notes

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0I don't even understand that...

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0IS he adding the 2 points or subtracting them?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1subtracting the 2 points. Maybe 2d is easier? say you are at (1,1) and you want to get to (2,2) how much to you move in the x and y? subtract to find you have to move (1,1) the (1,1) represents your slope. to get from one point on the line to another move over 1 and up 1. Or scale the 1,1 to get to any point on the line. example you are at 1,1 and you move 1/2 over and 1/2 up. You are still on the line

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. That makes sense I guess. I hope.

phi
 2 years ago
Best ResponseYou've already chosen the best response.1To continue the 2d example. if we say (x,y)= n(1,1) this means all points where y=x Say we want the line y= x+1 then we could say (x,y)= (0,1)+n(1,1)

phi
 2 years ago
Best ResponseYou've already chosen the best response.1Good luck. At least you have the answer, It is not a plane.

IsTim
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. Thanks for the help, and putting up with my lack of knowledge on the topic.
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.