Intersection Definition and 712 Threads

Hi, I need some help with this question: Find all values of \ k for which the lines do not intersect. \ (x-2,y+1,z-3) = (r,0,3r)\ and\ (x,y,z) = (2,1,4)\ +\ s(2,k,6) I put the first equation in vector form: \ (x,y,z) = (2,-1,3)\ +\ r(1,0,3) Now I know that if the direction...

Find symmetric equations of the line that passes through the point (0,1,2) and meets each of the lines x = y = z + 2 and x/-2 = (y+3)/1 = z/3. Those equations can be written as: r = (0, 0, 2) + t(1, 1, 1) r = (0, -3, 0) + s(-2, 1, 3) Now, I can't seem to find any direction to go with...

i have y=x^2-x and y=x from this x^2-x=x therefore: x^2=0, and x then equals zero. putting this info into y=x, y=0 this gives the points (0,0). however, in the answer book, it shows that the points of intersection are (0,0) and (2,2). how is it possible to do this?! appreciate any...

Original question: a) Find a vector function for the curve of intersection of the paraboloid z = 3x^2 + 2y^2 and the cylinder y = x^2. b) Show that this curve passes through (1,1,5) but not (3,3,9). I really have no idea how to do either parts of this question. Any help would be greatly...

I'm using the following equation to represent lines (x, y) = (start_x, start_y) + t((end_x, end_y) - (start_x, start_y)) I'm trying to find the interesection point of two lines written in this form. I have been able to solve for t and plug it back into the equation, but i get two values...

Hi, how do I find a tangent vector to the curve intersection of the surfaces 2x^2+2y^2-z^2=25 and x^2+y^2=z^2 which has positive x-direction? Thanks in advance.

The question is: Suppose W and X are subspaces of R^8. Show that if dimW=3, dimX=5, and W+X = R^8, then W \cap X = \{0\}. I can see this is obvious iff W and X are disjoint sets. If we add members of W to X in the usual way, and we get the new set W+X whose dimension is now 8 (given), then...

Let S and T be two spans of vectors, what's the general method to find a basis for the intersection of S and T (SnT)? Thanks

ok... first of all, I was discussing with my friend, he propose an argument of, if you have two N-Dimensional Spaces, (let's called it Sn1 and Sn2), they will form another M-Dimensional Spaces, which M is either 0 or M bigger or equal one smaller or equal N-1... what he said was that if Sn1...

Hello, How do I find the line of intersections of the two planes 7x - 2y + 3z = -2 and -3x + y + 2z + 5 =0, without having to resort to solving it by row reduction?

how do i find intersection of sin(x) and cos(x)? wat method do i use?

Could anyone help me summarize or if anyone knows good tricks in solving problems of lines intersecting with planes, etc, in 2d or 3d, the concept is same, but just want others opinion on what its basic idea is. i am able to do problems but i don't really understand them, i have to go back in my...