Recent content by tiki84626

Homework Statement Find the equations that satisfy the following properties: 1) f:(0,infinity) -> R is continuous and bounded, but f has no maximum and no minimum (that is global min and max). 2) k:[0,infinity) -> R is continuous, but k has no maximum and no minimum (again global min...

Can anybody think of equations that satisfy the following properties: 1) f:(0,infinity) -> R is continuous and bounded, but f has no maximum and no minimum (that is global min and max). 2) k:[0,infinity) -> R is continuous, but k has no maximum and no minimum (again global min and max).

Ok, so i get the equation for the line: (x,y,z) = (1 + 2t, 1 - t, 1 + t) x = 1 + 2t y = 1 - t z = 1 + t So, using the equations for our plane: x = 2y - z + 4 y = y z = z we get that: y = 1 - t z = 1 + t x = 1 + 2t = 2(1 - t) - (1 + t) + 4 t = 4/5 So, is their...

So, the equation for a line in space is: r = r0 +tv = (x0,y0,z0) + t<a,b,c> but once i have that, how do i solve for their intersection? and the angle between them? For their intersection, do i just solve the system of equations: x = x0 + ta y = y0 + tb z = z0 + tc x - 2y + z = 4 but what...

one can express a line by a pair of linear equations ax+by+cz+d=0 and a'x+b'y+c'z+d'=0 such that bc'-cb', ca'-ac', and ab'-ba' are not all zero. The line thus defined is parallel to the vector (bc'-cb', ca'-ac', ab'-ba'). Line through (x0,y0,z0) parallel to the vector (a,b,c)...

yeah i am having trouble figuring out how to find the equation for the path of the particle. From there I think it should be pretty easy, just setting them equal and finding their intersection. and then for the angle between them i can just use the dot product, but with what vectors?

Homework Statement The starting position of a particle in R3 is (1,1,1) and it's traveling with constant velocity (2,-1,1). Where does it hit the plane {(x,y,z)|x - 2y + z = 4}. And find the angle between the path of the particle and the plane. Homework EquationsThe Attempt at a Solution

Homework Statement I am having trouble understanding how I would go about finding all subgroups of index 2 in R*, the multiplicative group of nonzero real numbers. Any hints will be greatly appreciated. Homework Equations The Attempt at a Solution