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 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum Aug 5th 2013, 01:24 PM #1 Junior Member   Join Date: Aug 2013 Posts: 1 Equation of the line intercepting two planes I have two equations of planes . Lets say ax + by + cz = k and dx +ey + fz = k' When solving these two equations I should get an equation for a line. Now if I assume z = t then I can find x, y in terms of t parameter. That will give me a parametric equation for the line. But the problem is when a = b = 0 or ae = bd denominator become zero. So this solution is not correct for general case. I am not physics/math expert. I don't understand what to do next. Thank you if any one can guide me to find the equation of intersection between two plains. Thanks Chin   Aug 14th 2013, 07:32 AM   #2
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 Originally Posted by chinthaka I have two equations of planes . Lets say ax + by + cz = k and dx +ey + fz = k' When solving these two equations I should get an equation for a line. Now if I assume z = t then I can find x, y in terms of t parameter. That will give me a parametric equation for the line. But the problem is when a = b = 0 or ae = bd denominator become zero. So this solution is not correct for general case. I am not physics/math expert. I don't understand what to do next. Thank you if any one can guide me to find the equation of intersection between two plains. Thanks Chin
hello! CASE #1:

a = b = 0

cz = k
so z = k/c >>>> equation of a plane parallel to the xyplane

if we substitute this in the equation of the 2nd plane,
dx + ey + fk/c = k'
ey = -dx - fk/c + k'
y = (-d/e)x + (-fk/ec + k'/e)

for your 2nd case, i don't know >.< i'm still figuring it out..

EDIT:
okay. i think i have it figured out..

CASE #2:

i'm not sure if you've already tackled this in class.. but

a normal vector of plane 1 is <a, b, c>
a normal vector of plane 2 is <d, e, f>

if the 2 planes are parallel to each other, they have no line of intersection. To know if this is the case, the normal vectors of the 2 planes should have the same direction.. thus, they are scalar multiples of each other:
<a,b,c> = k<d,e,f>

Hence, k = a/d = b/e = c/f

rearranging this part:
a/d = b/e
we get:
ae = bd

so the 2 planes have no intersection

Last edited by ardiannef; Aug 14th 2013 at 07:51 AM. Reason: added answer for case 2  Tags equation, intercepting, line, planes Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post jackthehat Kinematics and Dynamics 5 Aug 12th 2015 02:18 PM cohen990 Advanced Electricity and Magnetism 0 Dec 13th 2012 08:55 AM dspaulding09 Electricity and Magnetism 0 Mar 1st 2010 03:56 PM Electron Special and General Relativity 1 Mar 8th 2009 06:31 PM ariol Kinematics and Dynamics 1 Jan 8th 2009 10:08 PM