replace x,y,and z with parametric forms and solve for t
t^2 + (5-3t)^2 + (3-2t)^2 = 6
14t^2 - 42 t + 28 = 0
(t-2)(t-1) = 0
t= 1 or 2 you get
(1,2,1) and (4,-1,-1)
Find the points of intersection of the line r=(0,5,3) +t(1,-3,-2) with the sphere x^2+y^2+z^2=6. Is the segment of the line between the intersection points a diameter of the sphere?
I'm not sure what I am doing wrong (obviously a lot) since I can't get the right answer with the back of my textbook. Please fix my errors and demonstrate the correct approach. Thanks!
x/1 = (y-5)/-3 = (z-3)/-2
x^2 = x=6
x^2-x-6=0
x=-3 or x=2