Determine a vector equation for the line through the points (-1, 4) and (2, -1).
I said: r= (-1,4) + (4,-5), tER, is that correct?
I think I found my mistake, I added wrong lol!
Yup, I got it, it should be r= (-1,4) + (3,-5), tER..yay for me! lol
what does tER mean, anyway?
To determine a vector equation for the line passing through the points (-1, 4) and (2, -1), you need to find the direction vector for the line.
The direction vector can be found by subtracting the coordinates of one point from the coordinates of the other point. Let's choose (-1, 4) as the starting point and (2, -1) as the ending point:
Direction vector = (ending point) - (starting point) = (2, -1) - (-1, 4)
= (2 - (-1), -1 - 4)
= (3, -5)
Now, to find the vector equation of the line, you can use the parameter t to represent any point on the line.
So, the vector equation for the line passing through the points (-1, 4) and (2, -1) is:
r = (-1, 4) + t(3, -5)
The variable t can take any real value, so t ∈ ℝ. This equation represents an infinite set of points that lie on the line passing through the given points.