Calc intersection of planes

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HelpWithCalc

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A) Identify 3 non-trivial planes that have single P.O.I. at P(-15, -6, -9)
B) Show that P is the POI by solving the related linear system
C) Identify 3 planes arranged in a "revolving door" such that the line of intersection contains point P
D) Solve the related linear system and show P is a possible solution

Please get back to me with the answers as soon as possible. really need.
 
HelpWithCalc said:
A) Identify 3 non-trivial planes that have single P.O.I. at P(-15, -6, -9)
B) Show that P is the POI by solving the related linear system
C) Identify 3 planes arranged in a "revolving door" such that the line of intersection contains point P
D) Solve the related linear system and show P is a possible solution

Please get back to me with the answers as soon as possible. really need.
Click to expand...
Please read the posting guide-line at:

https://www.freemathhelp.com/forum/threads/forums-submission-guidelines-from-the-sites-owner.109846/

Please share your work/thoughts - so that we know where to begin to help you.
 
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HelpWithCalc said:
A) Identify 3 non-trivial planes that have single P.O.I. at P(-15, -6, -9)
B) Show that P is the POI by solving the related linear system
C) Identify 3 planes arranged in a "revolving door" such that the line of intersection contains point P
D) Solve the related linear system and show P is a possible solution
Click to expand...
I personally hate these sorts of questions. There are infinitely many valid solutions and no one correct.
Here is an outline of a valid solution. Select two points \(\displaystyle S~\&~T\) different from \(\displaystyle P\) but \(\displaystyle P,~S~\&~T\) are not colinear.
Now let \(\displaystyle \vec u = \overrightarrow {PS} ~\&~\vec v = \overrightarrow {PT} \) Now find \(\displaystyle \vec{n}=\vec{u}\times\vec{v}\).
Now for plane one \(\displaystyle \pi_1: \vec{n}\cdot<x,y,z>=\vec{P}\cdot\vec{n}\). Please note that \(\displaystyle P\in\pi_1\).
To find a second and third plane follow that general outline being careful that not all three planes intersect in a line.

 
I suppose that the obvious solution
P1: x= -15
P2: y= - 6
P3: z= -9
would be considered "trivial".
 
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