If the product of the distances of the point (1, 2, 3) from the origin and the plane 2x - 3y + z + k = 0 is 7, then the value of k is

Step-by-step solution

Distance of the point (1, 2, 3) from the origin is d₁ = 1^2 + 2^2 + 3^2 = 14 Distance of the point (1, 2, 3) from the plane 2x - 3y + z + k = 0 is d₂ = |2(1) - 3(2) + 1(3) + k| 2^2 + (-3)^2 + 1^2 = |k - 1| 14 Given that d₁ d₂ = 7 14 |k - 1| 14 = 7 |k - 1| = 7 k - 1 = 7 or k - 1 = -7 k = 8 or k = -6 From the given options, k = 8 . Answer: 8