My Math Forum I can't find a vector perpendicular to two vectors

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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: 1,989 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: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Probably "cross product" is what he meant!

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