I have an exam in an hour and this one question is killing me! We enter our answers online so maybe I am just entering it wrong, but I can't for the life of me seem to get it right.. any help?
Find a linear function whose graph is the plane that intersects the xy plane along the line y=x+8 and contains the point (2,2,16)
Somehow, the solution shows
y= x + 8, we have b /= 0
-a/b = 1, -c/b=8
Since (2,2,16) lies on the place we can use the equation z=ax+by+c to get
16 = 2a + 2b + 16c
Solving the solution gives
a=2
b=-2
c=16
giving 2x – 2y + 16
I just don't get it!
Best Answer
Hint: pick any two points on the line. The cross product of the vectors from $(2,2,16)$ to the two points is a normal to the plane.