Answer:
8i - 7j - 9k
Step-by-step explanation:
We have three points:
A (1,0,3)
B (2,5,0)
C (3,1,4)
First of all, we write the following two vectors:
[tex]AB=(2-1,5-0,0-3)=(1,5,-3)[/tex]
[tex]BC=(3-2,1-5,4-0)=(1,-4,4)[/tex]
These two vectors connect A with B and B with C, and since these 3 points lie on the plane, the two vectors also lie on the plane.
Therefore, the cross product of these two vectors must be a vector perpendicular to the plane.
The cross product of the two vectors is:
[tex]AB \times BC = i(5\cdot 4 -(-3\cdot-4))+j(-3\cdot 1 -1\cdot 4)+k(1\cdot -4-5\cdot 1)=\\=8i-7j-9k[/tex]
And the equation of the plane can be found as:
[tex]8(x-a_x)-7(y-a_y)-9(z-a_z)=0\\8(x-1)-7(y-0)-9(z-3)=0\\8x-7y-9z=-19[/tex]
