Question

Consider the planes ax + by + cz = 0, bx + cy + az = 0 and cx + ay + bz = 0. Answer the following questions. 

(i) If a + b + c ≠ 0 and a² + b² + c² = ab + bc + ca, then the 

(A) three planes have no non-zero solution. 

(B) three planes intersect in a single point only. 

(C) three planes intersect in a line. 

(D) three planes are identical. 

(ii) If a + b + c = 0 and a² + b² + c² ≠ ab + bc + ca , then the 

(A) planes intersect in the line x = y = z. 

(B) planes do not have common point. 

(C) planes have infinitely many common points among which (1, 2, 3) is one such common point. 

(D) planes form a triangular prism. 

(iii) If a + b + c = 0 and a² + b² + c² = ab + bc + ca, then the 

(A) three planes have unique common point. 

(B) common solutions line on a line only. 

(C) three planes are identical. 

(D) three equations represent R³.

Answer 1

Correct option is (i) → (D); (ii) → (A); (iii) → (D)

(i) - (D) three planes are identical.

(ii) - (A) planes intersect in the line x = y = z

(iii) - (D) three equations represent R³