Finding an equation for a plane containing 3 points

[yecko]

Homework Statement

Homework Equations

https://answers.yahoo.com/question/index?qid=20120204205204AAEvo8V

The Attempt at a Solution

This is my attempt following the solution in the yahoo answer, yet it is incorrect...
Can anyone tell me if I have made mistake in any of the manipulation?
Any help is appreciated~~
Thanks!

 

[Orodruin]

You should double check your algebra.

 

[yecko]

I just multiplied the whole equation by -3 and manipulated all the signs... after i checked several times, i still can't find what is wrong...

 

[Orodruin]

Your algebra. You are not adding and multiplying correctly.

Write out every step.

 

[ehild]

I just multiplied the whole equation by -3 and manipulated all the signs... after i checked several times, i still can't find what is wrong...

Check the determinant.

 

[Mark44]

@yecko, when you calculate a cross product, it's a good idea to make sure that the vector you get is actually perpendicular to the two input vectors you're working with. This can be done very quickly, using the dot product. In the work you did, your calculated cross-product is <2, 2, -1>. This vector isn't perpendicular to either of the other two vectors, which means your calculation is incorrect.