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anonymous

  • 5 years ago

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.

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  1. anonymous
    • 5 years ago
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    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 <x,y,z> 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.

  2. anonymous
    • 5 years ago
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    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.

  3. anonymous
    • 5 years ago
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    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.

  4. anonymous
    • 5 years ago
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    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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