JEE Advanced 2025 Mathematics question
Let be the line of intersection of the planes given by the equations
2x + 3y + z = 4 and x + 2y + z = 5.
Let be the line passing through the point P(2, −1, 3) and parallel to . Let M denote the plane given by the equation
2x + y - 2z = 6.
Suppose that the line meets the plane M at the point Q. Let R be the foot of the perpendicular drawn from P to the plane M. Then which of the following statements is (are) TRUE?
Answer: (A),(C)
Solution
Direction of : . : (2 + t, −1 − t, 3 + t). In M: 2(2 + t) + (−1 − t) − 2(3 + t) = −3 − t = 6 ⇒ t = −9, Q = (−7, 8, −6), (A true). . Triangle PRQ is right-angled at R:
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