Find equation of the plane that contains following vectors v= v= 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.

Question

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.

anonymous · Answer

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.

anonymous · Answer

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 · Answer

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.

anonymous · Answer

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.