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 May 22nd, 2015, 09:44 AM #1 Newbie   Joined: May 2015 From: india Posts: 1 Thanks: 0 Linear algebra Sketch the plane x+y+z=1 on a positive octant where x=>0,y=>0 and z>=0. Do the same for x+y+z=2 on th same plane. What vector is perpendicular to these two planes? May 22nd, 2015, 10:28 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Have you done what this problem suggests- graph the two planes? In any case, there exist an infinite number of vectors that are perpendicular to a given plane- though they are all multiples of the same vector. One way to find such a perpendicular is to take two vectors in the plane and take the cross product of them. One plane is x+ y+ z= 1. It is easy to see that (1, 0, 0), (0, 1, 0), and (0, 0, 1) are points in the plane so the vectors <1, -1, 0>, which is from (0, 1, 0) to (1, 0, 0) and <1, 0, -1> which is the vector from (0, 0, 1) to (1, 0, 0). May 22nd, 2015, 03:34 PM   #3
Math Team

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Hello, Lekha!

Quote:
 Sketch the plane on a positive octant where Do the same for on the same graph. What vector is perpendicular to these two planes?

No graph is necessary.
In fact, "a positive octant" is unnecessary. May 22nd, 2015, 03:43 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2654 Math Focus: Mainly analysis and algebra A minor quibble: it's a normal vector, not the normal vector. $\langle 2,2,2 \rangle$ is another. Tags algebra, linear, planes 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 Channeltsui Linear Algebra 1 June 22nd, 2013 12:58 PM matqkks Linear Algebra 1 February 7th, 2012 01:39 PM ypatia Linear Algebra 2 March 5th, 2009 01:49 PM ypatia Linear Algebra 1 March 2nd, 2009 06:28 PM swat Algebra 1 November 14th, 2008 05:17 AM

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