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 April 8th, 2014, 07:21 AM #1 Member   Joined: Apr 2014 From: liverpool Posts: 37 Thanks: 4 vectors Plane P contains point A(1,2,3) and is parallel to u=2i +3j and v=i +2j -k Vector normal to plane is n=(3,a,b) Find suitable values for a and b. I get a=-2 b=-1, someone mentioned before they think the a value is wrong. I found it simply by dot product of u and n being equal to zero, then using same principle to find b with dot product of v and n. If anyone could confirm whether I am right or wrong, that would be great. April 8th, 2014, 10:11 AM   #2
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 Originally Posted by marks2014 I get a=-2 b=-1
I agree with these values. April 8th, 2014, 11:23 AM #3 Newbie   Joined: Apr 2014 From: Gevgelija Posts: 27 Thanks: 0 the normal vector n = (3, a, b) with the parallel vectors u = (2, 3, 0) and v = (1, 2, -1) has to be orthogonal i.e. in a scalar product has to give zero or you have the system 6 + 3 a + 0 b = 0 and 3 + 2 a - b = 0 so a resolves from the first equation as -2 and b resolves from the second equation as 3 - 4 = b = -1. everything is fine till here... The point A = (1, 2, 3) is not really on that plane P because (1, 2, 3) = g (2, 3, 0) + h (1, 2, -1) makes h = -3 from the third component and for g from the first two components you get two different values 1 = 2 g - 3 and 2 = 3 g - 6 so g has to be both 2 and 8/3 and it is conflict. April 8th, 2014, 11:26 AM   #4
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 Originally Posted by dobri The point A = (1, 2, 3) is not really on that plane P because (1, 2, 3) = g (2, 3, 0) + h (1, 2, -1) makes h = -3 from the third component and for g from the first two components you get two different values 1 = 2 g - 3 and 2 = 3 g - 6 so g has to be both 2 and 8/3 and it is conflict.
Who said P contains (0, 0, 0)? April 8th, 2014, 11:36 AM #5 Newbie   Joined: Apr 2014 From: Gevgelija Posts: 27 Thanks: 0 i say P contains A = (3, 5, -1) April 8th, 2014, 11:39 AM #6 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 But by saying that $P = \{g (2, 3, 0) + h (1, 2, -1)\mid g, h\in \Bbb R\}$ you are also saying that (0, 0, 0) lies in P. Tags 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 Punch Algebra 3 February 17th, 2012 08:57 PM gaussrelatz Algebra 3 November 6th, 2011 11:12 AM remeday86 Linear Algebra 2 July 9th, 2010 10:20 PM Peter1 Algebra 0 April 12th, 2009 01:22 AM Peter1 Math Books 0 December 31st, 1969 04:00 PM

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