- #1
irycio
- 97
- 1
Homework Statement
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?
Homework Equations
Come in (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 :)
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