The equation of the plane through the points \(A = (0,1,1), B = (1,1,0)\) and \(C = (1,0,3)\) can be written as \(ax + by + cz = 8.\)
Then what's the ordered triple \((a, b, c)\)?
+128475 See here : https://web2.0calc.com/questions/please-help_34243
The equation of the plane was found to be :
1x + 3y +1z - 4 = 0
So we can write
1x + 3y + 1z = 4 multiplying this through by 2 we get that
2x + 6y + 2z = 8
(a, b , c) = ( 2, 6 , 2)
Here's a way to do this without vectors:
plane equation: ax+by+cz=8
substituting x=0, y=1, and z=1 into the plane's equation:
a(0)+b(1)+c(1)=8
b+c=8
substituting the other two points in the same way:
a+b=8 ==> -a-b=-8
a+3c=8
add up these three equations:
b+c=8
-a-b=-8
a+3c=8
and you get:
(b+c)+(-a-b)+(a+3c)=(8)+(-8)+(8)
b+c-a-b+a+3c=8-8+8
(a-a)+(b-b)+(c+3c)=0+8
4c=8
c=2
b+c=8, and c=2, so b+2=8
b=6
a+b=8, and b=6, so a+6=8
a=2
therefore, the answer is (a, b, c) = (2, 6, 2)
