I'm very sory for asking another question, but I'm just preparing a final exam, which means that i solve something like 20 Problems a day, so I get confused from time to time
The Sphere S intersects the plane P in a circle. Find the radius of the circle. Given are:
Sphere S: x^2+y^2+z^2-2y-22z-103=0
Point C, centre of the circle of intersection: 6/7/8
and the plane P 2x+2y-z-18=0
My idea was first to find one direction vector of the plane, so for instance (1,-1,0) (one vector which lies on the plane)
Then I invented the line l, which goes from C farther on the plane an eventually hits the spehere.
To find where it hits the plane, I inserted the line in the equation of the sphere
As result, I get t^2=(70)^1/2
This value inserted for t and than substracted the beginning point C, the radius of my circle gets (140)^1/2 which is the wrong solution. The result must be 12 (so (144)^1/2).
As many times as I perform the calculation, I get the wrong solution, where is the flaw of my approach??