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Equation of a Plane - Vectors

  1. Oct 7, 2012 #1
    Hi all,

    How do you go about solving the following Question?

    Find an equation of the plane containing the point (1 , 1 , -1) and perpendicular to the line through the points (2 , 0 , 1) and (1 , -1 , 0).

    Stephen
     
  2. jcsd
  3. Oct 7, 2012 #2

    Direction vector of the line:

    $$\underline v:=(2,0,1)-(1,-1,0)=(1,1,1)$$

    So plane perpendicular to the above line is

    $$ax+by+cz+d=0\,\,,\,\,with\,\,\,0=(a,b,c)\cdot (1,1,1)=a+b+c=0$$

    But this plane also has to contain the point [itex]\,(1,1,-1)\,[/itex] , so it has also to be

    $$a+b-c+d=0$$

    Now try to continue from here and end the exercise.

    DonAntonio
     
  4. Oct 7, 2012 #3
    Thanks Don it makes sense.

    Stephen
     
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