If p is the perpendicular distance from origin to the plane passing through (1, 0, 0), (0, 1, 0) and (0, 0, 1), then what is 3p² equal to?

The plane through the intercepts (1,0,0), (0,1,0), (0,0,1) is x + y + z = 1, or x + y + z – 1 = 0. Perpendicular distance from origin = |–1|/√(1² + 1² + 1²) = 1/√3. So p² = 1/3, and 3p² = 1.