The coordinates of the point on the line (x−1)/2 = (y+1)/−3 = z/1 which is at a distance of √14 from the point (1, −1, 0) are:

The coordinates of the point on the line (x−1)/2 = (y+1)/−3 = z/1 which is at a distance of √14 from the point (1, −1, 0) are:

• A. (3, −4, 1) or (−1, 2, −1)
• B. (2, −2, 1) or (0, 0, −1)
• C. (4, −5, 2) or (−2, 3, −2)
• D. (1, 2, 3) or (−1, −2, −3)

Answer: A) (3, −4, 1) or (−1, 2, −1)

Explanation: General point is (2λ+1, −3λ−1, λ). Distance squared from (1, −1, 0) is (2λ)² + (−3λ)² + λ² = 14λ². Given distance is √14, so 14λ² = 14 → λ² = 1 → λ = ±1. If λ = 1, point is (3, −4, 1). If λ = −1, point is (−1, 2, −1).