JEE Main 2024 Mathematics question
Let the point, on the line passing through the points P(1, −2, 3) and Q(5, −4, 7), farther from the origin and at a distance of 9 units from the point P, be (α, β, γ). Then α² + β² + γ² is equal to:
Answer: (A)
Solution
Unit direction (2, −1, 2)/3; the farther point is (1, −2, 3) + 3(2, −1, 2) = (7, −5, 9), and 49 + 25 + 81 = 155.