Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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
 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
 2 years ago

This Question is Closed

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

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

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

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

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

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

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

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

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

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

phiBest ResponseYou've already chosen the best response.1
or 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.
 2 years ago

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

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

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

phiBest ResponseYou've already chosen the best response.1
I 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)
 2 years ago

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

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

phiBest ResponseYou've already chosen the best response.1
BA 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)
 2 years ago

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

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

IsTimBest ResponseYou've already chosen the best response.0
I 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.
 2 years ago

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

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

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

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

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

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

phiBest ResponseYou've already chosen the best response.1
Here 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.
 2 years ago

IsTimBest 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?
 2 years ago

phiBest ResponseYou've already chosen the best response.1
No 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
 2 years ago

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

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

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

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

phiBest ResponseYou've already chosen the best response.1
subtracting 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
 2 years ago

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

phiBest ResponseYou've already chosen the best response.1
To 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)
 2 years ago

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

IsTimBest ResponseYou've already chosen the best response.0
Ok. Thanks for the help, and putting up with my lack of knowledge on the topic.
 2 years ago
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
 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.