1.

Let A(0,6,6), B(6,6,0) and C(6,0,6) are three points and point D is moving on the line x+z-3=0=y. If G is centroid of DeltaABC, then minimum value of GD is

Answer»

`SQRT((47)/2)`
`sqrt((37)/2)`
`sqrt((57)/2)`
`sqrt((23)/2)`

Solution :G=(4,4,4)
Let D=(a,0,3-a)
`GD^(2)=(a-4)^(2)+(0-4)^(2)+(3-a-4)^(2)`
`=2a^(2)-6a+33`.
For minimum of `GD^(2),a=3/2`
`GD_("MIN") = sqrt(2.9/4-6.3/2+33)=sqrt(57/2`


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