Question

Linear algebra question
How do I demonstrate that the various coordinates are not aligned?

Answer 1

The coordinates are
A(1,3,6) B(2,2,7) and C(3,2,4)

Answer 2

When you say that the coordinates "are not aligned," that means that you can't draw a straight line that passes through all three points. Correct?

Answer 3

yes

Answer 4

To do this, all you need to do, is find the equation of a line passing through any two points, and show that the line doesn't pass through the third point. So let's take the first two points. Then\[(2,2,7)-(1,3,6)=(1,-1,1)\]so the line passing through points A and B is the line\[(1,3,6)+t(1,-1,1).\]Make sense so far?

Answer 5

yeah

Answer 6

Sorry for answering this late D:

Answer 7

The last part doesn't make sens to me... Can you explain further?
In the first part all you did was a substraction of the two coordinates (B-A).
But how did you reason in the other passage?