Explanation
Since, the centroid divides the line joining the orthocentre and circumcentre in the ratio 2:1
The coordinates of the centroid will be,
(93,93,123)
=(3,3,4)
Given, A=(1,2,−3),G(−3,4,5)
Therefore, AG=√(−3−1)2+(4−2)2+(5−(−3))2
and AG=√84=2√21
P is the centroid of △BCD
So, G divides AP in 3:1.
Let AG=3x, then GP=x
3x=2√21x=2√213
Now AP=AG+GP
⇒AP=3x+x
⇒AP=4x
⇒AP=4(2√213)=8√213
So, option A is correct.
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