Question

Match the following
I.The centroid of the triangle formed by (2,3,-1), (5,6,3),(2,-3,1) is
II. The circumcentre of the triangle formed by (1,2,3), (2,3,1) ,(3,1,2) is
III.The orthocenter of the triangle formed by (2,1,5) , (3,2,3),(4,0,4) is
IV.The incentre of the triangle formed by (0,0,0), (3,0,0) ,(0,4,0) is
I II III IV
1) d a b c
2) a b c d
3) d e b c
4) d a e c

• A. (2,2,2)
• B. (3,1,4)
• C. (1,1,0)
• D. (3,2,1)

Answer 1

The correct option is A (2,2,2)

$I.A(2,3,-1),B(-5,6,3),C=(2,-3,1)$
G=$(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3})=(3,2,1)$
II.ABC is equilateral
G=s=(2,2,2)