Equation of 3-dimensional plane

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Homework Help Overview

The problem involves finding the equation of a plane defined by a vector u and parallel to another plane formed by vectors v and w, along with the origin. The context is three-dimensional geometry and vector operations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the cross product to find the normal vector of the plane and question the correctness of the resulting equation. There is uncertainty about the interpretation of the problem regarding the relationship between the planes involved.

Discussion Status

Some participants have provided guidance on the normal vector and the general form of the plane's equation. There is ongoing clarification regarding the original problem statement and the implications of the calculations presented.

Contextual Notes

There are indications of potential confusion about the problem's wording and the implications of the vectors involved. A participant noted a typo in their equation, which may affect the discussion.

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Homework Statement



Find the equation of the plane through vectors u=(1,1,2) parallel to the plane containing v=(2,2,-1), w=(1,-1,0), and the origin.

Homework Equations





The Attempt at a Solution



I did the cross product of v x w = (-1,-1,-4).
Thus, my equation became -x-y-4z=-9. Is this correct? Thanks.
 
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bump...can anyone please see if I am right or wrong??
 
stanford1463 said:
bump...can anyone please see if I am right or wrong??

I'm not sure I understand the question here. Are you trying to find the equation of one plane (containing u) that is parallel to another plane (containing v,w. and the origin (0,0,0))? Or is there just one plane involved? Could you maybe repost the question in its original wording?
 
stanford1463 said:

Homework Statement



Find the equation of the plane through vectors u=(1,1,2) parallel to the plane containing v=(2,2,-1), w=(1,-1,0), and the origin.

Homework Equations


The Attempt at a Solution



I did the cross product of v x w = (-1,-1,-4).
Thus, my equation became -x-y-4z=-9. Is this correct? Thanks.

Yes, vxw=(-1,-1,-4) is the normal to the plane. So the equation of the plane is -x-y-4z=C for some constant C. If I put (1,1,2) into that, I don't get -9.
 
Ok thanks! Yeah, it was a typo, I meant -10.
 

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