A Metro pillar in Chennai extends along the line x = y = z. The foundation base is on the plane 2x + y + z = 12. At what coordinates does the pillar hit the foundation?

A Metro pillar in Chennai extends along the line x = y = z. The foundation base is on the plane 2x + y + z = 12. At what coordinates does the pillar hit the foundation?

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

Answer: B) (3, 3, 3)

Explanation: Since the pillar is along x = y = z, let the point be (k, k, k). It lies on the plane, so 2(k) + k + k = 12 → 4k = 12 → k = 3. The point is (3, 3, 3).