JEE Main 2019 Mathematics question
If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x − 5y = 15, then 2α − 3β is equal to:
Answer: (B)
Solution
Normal (1, −1, 1) × (2, −5, 0) = (5, 2, −3): plane 5x + 2y − 3z = 17.