(a) Find the distance between the parallel planes x+2y-2z+1=0 2x+4y-4z+5=0 (b) Find the radius of the circular section in which the sphere |r|=5 is cut by the plane t.(i+j+k)=3\sqrt{3} (c) Show that the plane 2x-2y+z+12=0 touches the sphere x\power{2}+y\power{2}+z\power{2}-2x-4y+2z-3=0.
(a) Find the distance between the parallel planes x+2y-2z+1=0 2x+4y-4z+5=0 (b) Find the radius of the circular section in which the sphere |r|=5 is cut by the plane t.(i+j+k)=3\sqrt{3} (c) Show that the plane 2x-2y+z+12=0 touches the sphere x\power{2}+y\power{2}+z\power{2}-2x-4y+2z-3=0.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.CT: Chapter Test
Problem 8CT
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(a) Find the distance between the parallel planes
x+2y-2z+1=0
2x+4y-4z+5=0
(b) Find the radius of the circular section in which the sphere
|r|=5 is cut by the plane
t.(i+j+k)=3\sqrt{3}
(c) Show that the plane 2x-2y+z+12=0 touches the sphere
x\power{2}+y\power{2}+z\power{2}-2x-4y+2z-3=0.
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