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June 9th, 2014, 07:16 AM   #1
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Planes and lines in 3D

Hi everyone !
I'd like to know if someone could help me :
If we take two planes and , and call (D is a line). How can we prove that a random plan P contains D if and only if P has the following cartesian equation :
Thanks a lot !!
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June 9th, 2014, 08:50 AM   #2
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Hi, it is clear that any point whose satisfy both equations and lies on their line of intersection. Clearly the coordinates of such point satisfy the equation ,
where and are arbitrary constants which may assume all real values except that of them may not be zero simultaneously.


That equation represents a family of planes passing through the intersection of given planes.
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June 11th, 2014, 03:19 AM   #3
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Thanks ! And how do you find the equation of a plan P which contains a line D and a point M(a,b,c) (Assuming M is not on the line D)?
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June 11th, 2014, 09:17 PM   #4
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Anyone help? thanks a lot
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June 13th, 2014, 02:00 AM   #5
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Take help from online tutoring .There are various sites which are very cheap try it .
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June 13th, 2014, 03:03 AM   #6
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Ignore the previous post; there is nothing wrong with you asking the question and we'll happily help. I'll see if I can get an answer to you soon (unless someone else on the forum beats me to it )
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June 13th, 2014, 11:04 AM   #7
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ok, just wait.

you have the line and the point then you have three non-collinear points then you have three equations and 4 variables, then you solve the system for any three of the variables in terms of the fourth (which is not be zero). substituting these values in the general equation () next dividing through the letter and you have the equation.
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