Question

If (3, 2, -1), (4, 1, 1) and (6, 2, 5) are three vertices and (4, 2, 2) is the centroido of a tetrahedron, find the fourth vertex.


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Answer 1

Step-by-step explanation:

Answer is in attachment

Hope it helps

Answer 2

Step-by-step explanation:

The three vertices of tetrahedron is (0,0,0) , (6,−5,−1) and (−4,1,3)

Let the fourth vertex be (x,y,z)

Given that the centroid is (1,−2,5)

So we have

4

x+0+6−4

=1 ,

4

y+0−5+1

=−2 and

4

z+0+3−1

=5

⇒x=2 , y=−4 and z=18

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