What is the distance between the plane #x+y+z=0# and the sphere of unit radius with centre #(1, 3, 5)# ?
1 Answer
Dec 16, 2017
Explanation:
The normal to the plane
#p(t) = (1,3,5)+t(1,1,1) = (t+1, t+3, t+5)#
So when
#p(-3) = (-2, 0, 2)#
which is on the plane
The distance between
#sqrt(3^2+3^2+3^2) = sqrt(27) = 3sqrt(3)#
The line segment joining these two points intersects the sphere at a distance of