# lines

1. ### Lines through triangle

http://i44.tinypic.com/1ivzb.jpg See image A above The black triangle is an isosceles triangle. Consider the lengths of the parts of green and red line which are inside of the black triangle. If I move the green and red lines together up or down, along the midaxis of the symmetric triangle, do...
2. ### geometry tricky: 2n dota and 3n lines

let's have 2n dots and 3n straight line in the plane, with n positive integer. proof that exist at least one point P in the plane such that the sum of the distances of P to the 3n lines is lower that the sum of the distances of P to the 2n points ! I have started with 2 dots two lines, and two...
3. ### Proof by induction: n choose 3 triangles are formed by n lines

Prove: n choose 3 triangles are formed by n lines such that no 3 lines can intersect at the same point. I'm required to prove this by induction, I know it's really easy to prove without it. I know the base case, but the induction step seems tricky. I'm finding it hard to figure out how many new...
4. ### Vectors - shortest distance between two 3d lines

'Show that the shortest distance between the line with equations (x + 4)/3 = (y - 3)/2 = (z + 6)/5 and the line with equations x - 2y - z = 0, x - 10y - 3z = -7 is 1/2 sqrt 14.' I rewrote the equations in vector form: -4i + 3j - 6k + s(3i + 2j + 5k) 7i/2 + 7k/2 + t(-2i + J - 4k) I found the...
5. ### Slope of all Tangent Lines through the origin. Method 1.

https://skydrive.live.com/redir?resid=DB0189AA1CD22777!139676&v=3 https://skydrive.live.com/redir?resid=DB0189AA1CD22777!139675&v=3 To start with I graphed the equation 1+(x-1)^2. I see that the origin of the parabola is shifted one unit up and one unit to the right and the parabola faces...
6. ### Distance Between a Line and a Plane

Hey everyone, this is my first post here, so here goes: I'm stuck on a question right now for an assignment, the question is: Show that the line: x = 2 + t, y = -3 + 2t, z = 1 + 4t is parallel to the plane 2y - z = 1. What is the distance between the line and the plane? I determined that...
7. ### IBV23 find point P the intersection of 2 vector equations of lines

r_1 (5 \ 1)+\lambda (3 \ -2) and r_2 (-2 \ 2)+t (4 \ 1) presume one way to do this is turn these into line equations y=-\frac{2}{3}x+6 y=\frac{1}{4}x+\frac{3}{2} then x=\frac{46}{3} and y=\frac{16}{3}
8. ### Simple question on lines.

Explain why two straight lines in spacecan intersect at most at one point. We know that a line is composed of aninfinite set of points. Now, we have line A and line B.(Of the samelenght, but it doesn't matter) We will have line A, which isstationary, with any desidered position. Now, we...
9. ### Vector equations of lines

Can someone please help me with these problems? (1) Let A, B, C be the vertices of a triangle. Let a, b, c be their position vectors respectively. Find the equations of the lines through each vertex, perpendicular to the opposite side. (2) Find the equations of the perpendicular bisectors of...
10. ### Fermat's last theorem ( My own Evidence 5 lines one a4)

! before start read please read about problem ! >>>http://en.wikipedia.org/wiki/Fermat's_Last_Theorem People who see final picture of my evidence - think that it is very easy :) At the end I showed link - 1 000 000 USD prize for person who will solve similar equation . I need...
11. ### Equations of these lines and planes

Hi. For lines, i know primarily we need a point, and a vector parallel to the line. But for this question, Find the equation of the line through (2,1,0) and perpendicular to both i+j and j+k. How do i derive the parallel vector. What doe sit mean if the line is perpendicular to i+j and j+k ...
12. ### Find the shortest distance between the lines:

Sorry again if this is a noobie post. In R3, find the shortest distance between the lines: l1 = x (2, -1, 3) + t(1, -1, 4) l2 = x (1, 0, 1) + t(1, -1, 4) Unless I am mistaken I would take vector 1 to be (1, -1, 4) and vector 2 to be (1, -1, 4) as well. Using the equation distance = |P1P2...
13. ### Parametric representation of lines.. (simple)

I just can't get my head around this, what am I doing wrong. for example, given that, r(t) = (1-t)r0 + t(r1) and say we have a line segment: (-2,-1) to (1,2) How is it that x = -2 + 3t and y = -1 +3t r(t) = (1-t)<-2,-1> + t<1,2> I am not seeing how this expression becomes: <-2+3t, -1+3t>...
14. ### Theta is the acute angle between these regression lines.

The equation of the line of regression of y on x is 3x +2y -26 =0 and that of the line of regression of x on y is 6x + y - 31 =0. Find the angle theta between these two regression lines with the help of correlation coefficient and it's square.I have calculated it with the help of slope formula...
15. ### How to put a box around multiple equations on multiple lines?

I want to put one box around 5 equations where each equation is on a separate line and the equations are aligned. Also, outside of the box and on the right side of the page (sort of center from the box, say five equations I like the label to be on the same line as the third equation) I would...
16. ### Determining whether the lines are parallel, intersect, or skew

I have a problem where i don't have the solution to since i like to practice odd problems. I am not sure if i have done this correctly. Determine whether the lines L1: 1 + t, y = 2 + 3t, z = 3 + t L2: 1 + t, y = 3 + 4t, z = 4 + 2t are parallel, intersecting, or skew. If they intersect find...
17. ### Contour lines

Hey guys!!!Could you help me at this exercise??? (Worried) Draw some contour lines in the (x, y)–plane of the function h(x,y)=(a*(x+y))/(x^2+y^2+a^2). Thanks in advance!!!
18. ### finding equations for two lines through the origin

The questions reads Find equations for two lines through the origin that are tangent to the curve x^2-4x+y^2+3=0 ,, Not sure what the question is asking.. :( Any help?
19. ### Tangent Lines of a Nondegenerate Conic

If I fixed a nondegenerate conic, (e.g. XZ-Y^2=0), then I want to show that the set of tangent lines of this conic (i.e. the lines that intersect this conic with multiplicity 2) form a subvariety in the projective space P2. I know an arbitrary line looks like aX+bY+cZ=0, but when I plug that...
20. ### explanation of how to find vector field lines

Hello, I have a function f=(x^2+y^2)/z , F=grad(f)=2x/z i + 2y/z j + (x^2+y^2)/z^2 k. I am supposed to find the field lines of F but I can't really understand how to do this from reading the book. I did it in 2D and kind of got it but in 3D I am lost. Any help here is really appreciated.