You have made some mistake in calculations.
Did you use the cross product?
I've got this exercise where I'm required to describe the equation of the plane determined by the fact that the following
three points lie in it: (−7, 1, 0), (2, −1, 3), (4, 1, 6).
What i've done for it is as followings:
To describe the equation of the plane we require a point in the plane and a vector that is orthogonal to every vector in the plane. The vectorn is said to be normal to the plane.
We suppose our point in the plane to be
We chose n the normal vector to be on of our given three points.
Now we have discovered a point within the plane and a normal we can carry out the equation of the form
Well thats my attempt at the question i not quiet sure that i've answered it fully but i think i did most part correctly. I would appreciate any advice/help with it with the question it self and my answer (if it could be built on).
Thanks a lot !
where as shown i obtained 12, 21 and -22 by calculating the normal. I then substitute a vector in the plane, i.e 4,1,6), giving you an equation
The equation can now be rewritten to the form
I'm not sure how to reorganize that equation to evaluate the d mentioned above. Any help /push in the right direction would be great!
Once this is done then I should be able to check my equation by seeing whether each of the given three points in the plane satisfies it right ?
Thanks a bunch
So i've got a new equation that needs to be determined by the the fact the following three points lie in it: and So i find two vectors that lie in the plane.
To find a normal vector we need to take the cross product
This is the normal vector to the plane
I just want to check that what i've done is correct so far?