anonymous
  • anonymous
Find equation of the plane that contains following vectors v= <2,1,4> v= <3,-1,5> is it 9x+2y-5z? I mean I just need to make the cross product? as there are no point to use to substitute to general formula.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
The cross product will give you a vector which is perpendicular to the plane. Since you know that this vector is perpendicular to your plane, the dot product of it and any point in the plane will be 0. Therefore your plane will be all the points which are solutions to the equation 9x + 2y - 5z = 0.
anonymous
  • anonymous
this quation is not complete, no particular solotion for this problem. However, the general solution is 9x+2y-5z=d, where d is any costant.
anonymous
  • anonymous
Jack, I disagree. Since the plane contains those vectors (not parallel to them) the plane goes through the origin. Therefore the constant d in your example must be 0.

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anonymous
  • anonymous
polpak, I disagree with u. All the parallel planes 9x+2y-5z=d contain the vectors v= <2,1,4> and v= <3,-1,5>, where d is any costant.

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