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IsTim
 3 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.
IsTim
 3 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.

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

IsTim
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0@Phi What is elimination?

IsTim
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1what kind of math are you studying?

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

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

phi
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0I had difficulties understanding the course. I don't exactly know.

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

phi
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0What's an equation of a line?

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

phi
 3 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
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1*should be BA as the label

IsTim
 3 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
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1See if this helps http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfLines.aspx

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

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

IsTim
 3 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
 3 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
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1Look at Example 1 in Paul's notes

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

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

phi
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0Ok. That makes sense I guess. I hope.

phi
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1Good luck. At least you have the answer, It is not a plane.

IsTim
 3 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.
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