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Find-the-shortest-distance-from-the-plane-r-n-q-to-the-sphere-r-r-0-R-

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Question Number 31264 by ajfour last updated on 04/Mar/18
Find the shortest distance from the plane r^� .n^� =q to the sphere ∣r^� −r_0 ^� ∣=R .
Findtheshortestdistancefromtheplaner¯.n¯=qtothesphere∣r¯−r¯0∣=R.
Commented by ajfour last updated on 04/Mar/18
Commented by ajfour last updated on 05/Mar/18
let the shortest distance be d_s . ∣(r_0 ^� −r_A ^� ).n^� ∣=R+d_s ⇒ d_s =((∣r_0 ^� .n^� −q∣)/(∣n^� ∣))−R .
lettheshortestdistancebeds.∣(r¯0−r¯A).n^∣=R+ds⇒ds=∣r¯0.n¯−q∣∣n¯∣−R.

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