# Math Help - intersection

1. ## intersection

From the point drawn normals to the two planes and have the equations and . A plane containing the two normals. Determine the intersection, and . (ON-system.) ima answer the intersection

how shall i take dot product on this one?

2. ## Re: intersection

Hey Petrus.

If two planes intersect then they are equal to each other.

Can you solve the linear system corresponding to the intersection?

(Hint: for the third plane the normal of this plane will correspond to the cross product of the two other normal vectors).

3. ## Re: intersection

Sorry idk what to do on this problem.. I cant solve the equation

4. ## Re: intersection

Recall that a plane in three dimensions has the form ax + by + cz = d for some constants a,b,c,d.

Now you just have to solve a linear system with three of these equations where you solve for x given the system Ax = b.

5. ## Re: intersection

Do u mean like
Y=8+2z?
wha i thought i need to find the third plane to solve the linear equation

6. ## Re: intersection

That is one equation of a plane where Y - 2z = 8 where a = 0, b = 1, c = -2 and d = 8 in this particular example.

7. ## Re: intersection

I serious dont understand this one, any tips what i should read to get this... Im clueless

8. ## Re: intersection

Originally Posted by Petrus
From the point drawn normals to the two planes and have the equations and . A plane containing the two normals. Determine the intersection, and . (ON-system.) ima answer the intersection

Actually I have not idea exactly what that says.
I think it means that $P$ is not on either plane: $\Pi_1:N_1\cdot (R-Q)=0~\&~\Pi_2:N_2\cdot (R-S)=0$.

The plane $\Pi : (N_1\times N_2)\cdot (R-P)=0$ contains the $P$ and the two normals

If that is not what you are asking, try to clear it up please.

9. ## Re: intersection

From the plane P draw the normal to the both i1 and i2 that have the equation x-y+5z=2 and y-2z=8. A plane i3 got the both normal. Decide the intersection between i1,i2 and i3 ( on bas)
Thats My translate sorry i hope u understand but the answer shall be
111/14,47/7,-9/14

10. ## Re: intersection

Originally Posted by Petrus
From the plane P draw the normal to the both i1 and i2 that have the equation x-y+5z=2 and y-2z=8. A plane i3 got the both normal. Decide the intersection between i1,i2 and i3 ( on bas)
Thats My translate sorry i hope u understand but the answer shall be
111/14,47/7,-9/14

Again, if we understand each other, then solve
$\begin{gathered} 3x - 2y - z = - 1 \hfill \\ x - 2y - z = - 2 \hfill \\ y - 2z = 8 \hfill \\ \end{gathered}$

Yes

12. ## Re: intersection

Did you take Plato's advice and solve the linear system?

If you need to check your work use a program like Octave to do so which is free and you can download GUI octave for the MATLAB style window.

13. ## Re: intersection

If i understand right then x =-3/2 then ima solve rest somehow ? Is that program big? I got a really cheap pc so and its alredy so slow

14. ## Re: intersection

Since this is a 3x3 system with Ax = b we know that x = A^(-1)b and there are many websites that do matrix multiplication and inverse calculations.

Here is one of them:

3x3 Inverse Matrix Calculator & Calculation

3x3 Matrix Multiplication Calculator, 3x3 Matrices Calculation Formula