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TS EAMCET 20-July-2022 Shift 1 Solved Paper
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© examsnet.com
Question : 62
Total: 160
A
(
1
,
1
,
1
)
,
B
(
1
,
−
4
,
3
)
,
C
(
2
,
−
2
,
0
)
and
D
(
8
,
1
,
4
)
are the vertices of a tetrahedron.
G
1
,
G
2
,
G
3
and
G
4
are the centroids of the faces
A
B
C
,
B
C
D
,
C
D
A
and
D
A
B
. Then the centroid of the tetrahedron having
G
1
,
G
2
,
G
3
,
G
4
as its vertices is
(
12
,
−
4
,
8
)
(
4
,
−
4
3
,
8
3
)
(
2
,
−
2
3
,
4
3
)
(
3
,
−
1
,
2
)
Validate
Solution:
👈: Video Solution
Let
A
(
1
,
1
,
1
)
,
B
(
1
,
−
4
,
3
)
,
C
(
2
;
−
2
,
0
)
and
D
(
8
,
1
,
4
)
are the vertices of a tetrahedron.
Since,
G
1
is the centroid of face
A
B
C
∴
G
1
≡
(
x
1
+
x
2
+
x
3
3
,
y
1
+
y
2
+
y
3
3
,
z
1
+
z
2
+
z
3
3
)
G
1
≡
(
1
+
1
+
2
3
,
1
−
4
−
2
3
,
1
+
3
+
0
3
)
G
1
≡
(
4
3
,
−
5
3
,
4
3
)
Now,
G
2
is the centroid of face
B
C
D
,
∴
G
2
=
(
1
+
2
+
8
3
,
−
4
−
2
+
1
3
,
3
+
0
+
4
3
)
G
2
=
(
11
3
,
−
5
3
,
7
3
)
Also,
G
3
is the centroid of the face
C
D
A
.
∴
G
3
=
(
1
+
2
+
8
3
,
1
−
2
+
1
3
,
1
+
0
+
4
3
)
G
3
≡
(
11
3
,
0
,
5
3
)
Also,
G
4
is the centroid of the face
D
A
B
,
∴
G
4
=
(
1
+
1
+
8
3
,
1
−
4
+
1
3
,
1
+
3
+
4
3
)
G
4
≡
(
10
3
,
−
2
3
,
8
3
)
Now, centroid of tetrahedron having
G
1
,
G
2
,
G
3
and
G
4
as its vertices.
G
=
(
4
3
+
11
3
+
11
3
+
10
3
4
,
−
5
3
−
5
3
+
0
−
2
3
4
,
4
3
+
7
3
+
5
3
+
8
3
4
)
∴
G
=
(
3
,
−
1
,
2
)
© examsnet.com
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