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Question

Find the points on the line x+23=y+12=z32 at a distance of 5 units from the points (1,3,3).

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Solution

General point on the
line would be

(3λ2,2λ1,2λ+3)
it is at distance 5 units
from (1,3,3)
(3λ3)2+(2λ4)2+(2λ)2=5

17λ2+2534λ=25
17λ(λ2)=0
λ=0 or λ=2

Posible points :-

(2,1,3),(4,3,7)

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