(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Three-dimensional, euclidean space. We've got 2 non-parallel planes:

[tex] \vec{OX} \cdot \vec{b_1}=\mu_1[/tex] and [tex] \vec{OX} \cdot \vec{b_2}=\mu_2[/tex]. Find all the points Y such that Y lies on the first plane and Y+[tex]\vec{a}[/tex] lies on the 2nd one. What did you get?

2. Relevant equations

Come in (3.)

3. The attempt at a solution

So we start with such equations:

[tex]\vec{OY} \cdot \vec{b_1}=\mu_1 [/tex] AND [tex]\vec{OY} \cdot \vec{b_2} + \vec{a} \cdot \vec{b_2}=\mu_2 [/tex].

Simple manipulation and we get:

[tex] \vec{OY} \cdot (\vec{b_1} - \vec{b_2} )= \mu_1 - \mu_2 +\vec{a} \cdot \vec{b_2} [/tex] (substracted 2nd equation from the 1st one).

And this is where I get stuck, I have no idea how to have [tex]\vec{OY} [/tex] on one side and the rest on the other.

Thx in advance for your help!

E: I'm not even sure that what I've got so far is correct-I believe that those points should all lie on one line, and I've got a plane again. But what I believe in geometry is not necessarily true :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Euclidean geometry-2 planes

**Physics Forums | Science Articles, Homework Help, Discussion**