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 November 10th, 2010, 07:54 AM #1 Member   Joined: Apr 2010 Posts: 91 Thanks: 0 Line/plane problem (vectors) A line passes through the point P (3, 4, 1) and has direction vector (1, 2, 2). The point Q is also on and lies the same distance above the plane z = 4 as P is below that plane. What are the coordinates of Q? If P and Q are on the same line, then how can Q be above the plane and P below it? (I drew a horizontal line). November 10th, 2010, 01:29 PM   #2
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Re: Line/plane problem (vectors)

Quote:
 Originally Posted by TsAmE A line passes through the point P (3, 4, 1) and has direction vector (1, 2, 2). The point Q is also on and lies the same distance above the plane z = 4 as P is below that plane. What are the coordinates of Q? If P and Q are on the same line, then how can Q be above the plane and P below it? (I drew a horizontal line).
First write out the equation for the line:
A=P + Vt, where P=(3,4,1) and V=(1,2,2)
On the plane, the z coordinate for A is given by 1 + 2t = 4, or t=1.5. To get Q, use t=3 (1.5 above) so:
Q=(6,10,7)

To answer your second question, a line in the plane z=4 would have a constant 4 for the z coordinate, i.e. the vector V would have 0 for the z coordinate and P would have 4 for the z coordinate. Tags line or plane, problem, 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 shizei Linear Algebra 4 October 28th, 2013 08:23 AM sara213 Calculus 2 November 27th, 2011 10:57 AM AFireInside Algebra 2 September 11th, 2011 03:25 PM AFireInside Physics 1 September 9th, 2011 07:16 PM Hypatia Calculus 2 July 20th, 2008 05:36 PM

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