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 June 21st, 2014, 04:00 PM #1 Member   Joined: Nov 2013 Posts: 34 Thanks: 1 I can't find a vector perpendicular to two vectors I have two lines: LINE A x=-t y=2+t z=7+3t LINE B(x-3)/3 = y/-3 = (z-2)/9Line B, as far as I know is: x=3t+3 y=-3t z=9t+2 I need to find the equation of the plane which contains LINE A and LINE B. First of all, I should find a vector perpendicular to both lines, which will let me make a equation of the plane I'm looking for. So, Direction vector for LINE A is <-1,1,3> Direction vector for LINE B is <3,-3,9> When I make the dot product for finding a vector perpendicular to both lines, I get this: -x+y+3z=0 3x-3y+9z=0 What I normally do is to solve the system and then find the equation of the plane with a point. But this system, can't be solved. What do you recommend me to do? Thank you very much. June 21st, 2014, 05:34 PM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Line A for t=0 you get (0,2,7) Line B for t=0 you get (3,0,2) for t=1/3 you get (4,-1,5) $\displaystyle \ell(0,2,7)+\mu(3,0,2)+(4,-1,5)=(3\mu+4,2\ell-1,7\ell+2\mu+5)$ $\displaystyle\left\{\begin{matrix}x=3\mu+4\\y=2 \ell-1\\z=7 \ell+2\mu+5\end{matrix}\right.$ so plugging in the two first equation to the third one you get $\displaystyle z=7\cdot \frac{y+1}{2}+2\cdot\frac{x-4}{3}+5$, do the computations because I want to go to sleep......... Thanks from lauchagonzalez June 22nd, 2014, 10:11 AM #3 Member   Joined: Nov 2013 Posts: 34 Thanks: 1 Thank you ZardoZ! June 22nd, 2014, 12:16 PM   #4
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Quote:
 When I make the dot product for finding a vector perpendicular to both lines, I get this: -x+y+3z=0 3x-3y+9z=0
Didn't you mean cross product? June 23rd, 2014, 05:09 AM #5 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Probably "cross product" is what he meant!  Tags find, perpendicular, vector, 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 bigwave Algebra 3 August 25th, 2013 09:50 PM furor celtica Calculus 3 February 9th, 2012 01:10 PM bilano99 Calculus 2 February 8th, 2012 01:49 PM eftim Linear Algebra 1 September 26th, 2010 01:12 PM amp88 Algebra 1 August 19th, 2009 08:54 AM

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