Let position yector of point B be b. Let position vector of point C be c. Let position vector of point D be d. Position vector of centroid of △BCD=‌−
∧
i
+2
∧
j
−3
∧
k
‌
b+c+d
3
=‌−
∧
i
+2
∧
j
−3
∧
k
d=‌−3
∧
i
+6
∧
j
−9
∧
k
−b−c d=‌−3
∧
i
+6
∧
j
−9
∧
k
‌−(−2
∧
i
+
∧
j
+3
∧
k
+3
∧
i
+2
∧
j
−
∧
k
) =‌−3
∧
i
+6
∧
j
−9
∧
k
−
∧
i
−3
∧
j
−2
∧
k
=−4
∧
i
+3
∧
j
−11
∧
k
Let position vector of centroid G of tetrahedron ABCD be g. g‌=‌