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 October 30th, 2016, 12:36 PM #1 Member   Joined: Oct 2016 From: Slovenia, Europe Posts: 52 Thanks: 5 difficult task with vectors, lines and planes Find all the points on the z axis which lies on the same distance from planes 2x+3y+z=1 and x+y+z=0. I really do not know how to start solving it, although I am familiar with the basic rules and formulas of planes, lines etc. Please help me!  October 30th, 2016, 01:45 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,924 Thanks: 2203 Have you tried using this formula for the distance from a point to a plane? October 30th, 2016, 01:48 PM #3 Global Moderator   Joined: May 2007 Posts: 6,806 Thanks: 716 Point on z axis has coordinates (0,0,z). Line through point perpendicular to 2x+3y+1=1 is has equation (0,0,z)+s1(2,3,1) where $\displaystyle s1=\frac{s}{\sqrt{14}}$. For plane x+y+z=0, line is (0,0,z)+s2(1,1,1) where $\displaystyle s2=\frac{s}{\sqrt{3}}$. In the above |s| is the common distance form the point to the planes. You then have two sets of equations in two unknowns when you set the points from the lines onto the planes. $\displaystyle s\sqrt{14}+z=1$ and $\displaystyle \pm s\sqrt{3}+z=0$ The plus-minus takes care of the fact that |s| is asked for. Last edited by mathman; October 30th, 2016 at 04:19 PM. Reason: additional material Tags difficult, lines, planes, task, vectors Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post avniu Geometry 0 July 18th, 2015 06:35 AM Cyberdollar Geometry 6 June 13th, 2014 11:04 AM Dan3500 Calculus 1 September 26th, 2013 07:30 AM livestrong136 Calculus 5 May 25th, 2012 07:26 AM NiCeBoY Algebra 0 October 30th, 2008 09:59 PM

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