Question

Do the points A(2,1,5), b(-1,-1,10), and c(8,5,-5) define a plane? Explain why or why not.

Answer 1

use elimination to find if the three points are independent (not collinear)

Answer 2

Elimination?

-I think no, because there is no position vector or a direction vector.

Answer 3

Pi?

Answer 4

@Phi What is elimination?

Answer 5

http://www.wolframalpha.com/input/?i=rref+%7B%282%2C1%2C5%29%2C+%28-1%2C-1%2C10%29%2C+%288%2C5%2C-5%29%7D

Answer 6

Sorry if I sound persistent, but I still don't understand (I have looked through the link).

Answer 7

what kind of math are you studying?

Answer 8

Vectors, of Vectors and Calculus.

Answer 9

Specifically, Lines and Planes.

Answer 10

Do they teach you about independent vectors? How to tell if two vectors are independent?

Answer 11

I had difficulties understanding the course. I don't exactly know.

Answer 12

equations of lines is the lesson (specifically)

Answer 13

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.

Answer 14

What's an equation of a line?

Answer 15

I'm just looking thru my textbook here, but I can only see equation of a plane. I'll use Google now though.

Answer 16

y=mx+b? How does that work for a 3-space point?

Answer 17

I think you do A + n(B-A)
e.g. (2,1,5)+n ((-1,-1,10)-(2,1,5))
where n is any value (a scalar)

Answer 18

You mean like a vector equation?
[x,y,z]=[xo,y0,zo]+t[a1,a2,a3]+s[b1,b2,b3]

Answer 19

But that wouldn't make sense to me...Aren't the ones with scalar multipliers direction vectors?

Answer 20

B-A points in the direction from A to B

you scale it to move along it.
Add A so the direction vector starts at A rather than the origin
so
A+ n(B-A)