# A Monotone Test problem

1. May 18, 2009

### Asuralm

Hi all:
Hi all:

Assume in 3D space there is a point $$v=[v_x, v_y, v_z]$$ , and a normal vector associate with it as $$n=[n_x, n_y, n_z]$$ . A line function is defined as $$u=w+t\cdot$$ where $$w=[w_x, w_y, w_z]$$ is a point, and $$l=[l_x, l_y, l_z]$$ is the normalized direction of the line. l and n are normalized. Assume there is a function defined as:

$$K =\frac{(u-v)\cdot n}{||u-v||^2}$$

My question is when point u varies on the line, is the function K varies monotonically???

I've tried to compute $$\frac{dK}{dt}$$ , but I can't really see if it's monotone or not, can some one help me please?

Thanks

2. May 18, 2009

### tiny-tim

Last edited by a moderator: Apr 24, 2017
3. May 18, 2009

### Asuralm

Sorry tiny-tim, but I don't get any useful help from the last thread though.

The problem is not as simple as it looks like first time.

Last edited by a moderator: Apr 24, 2017