Question

If a plane meets the coordinate axes at the points (a, 0, 0), (0, b, 0) and (0, 0, c), then its equation is

x/a + y/b +z/c = 1

(i) A plane cuts the coordinate axes at A(2, 0, 0), B(0, 3, 0) and C(0, 0, 1). Then the area of the triangle ABC is 

(A) 11/2 

(B) 9/2 

(C) 7/2 

(D) 5/2

(ii) The volume of the tetrahedron OABC, where O is the origin, is 

(A) 6 

(B) 1 

(C) 2 

(D) 1 6

(iii) The centroid of tetrahedron OABC is 

(A) 1/2,3/4,1/4

(B) 1/4,3/4,1/4 

(C) 2/3,1,1/3

(D) 1/3,1/3,1/3

Answer 1

Correct option is (i) → (C); (ii) → (B); (iii) → (A)

(i) - (C) 7/2

(ii) - (B) 1

(iii) - (A) 1/2,3/4,1/4