Exams › JEE Main › Maths

A moving plane always contains the fixed point (1, 2, 3). The set of points that are the perpendicular projections of the origin onto this plane is described by

1. x² + y² + z² − 14 = 0
2. x² + y² + z² + x + 2y + 3z = 0
3. x² + y² + z² − x − 2y − 3z = 0
4. None of these

Correct answer: x² + y² + z² − x − 2y − 3z = 0

Solution

The correct option represents a sphere centered at the point (1, 2, 3) with a radius that ensures the origin's perpendicular projection lies on the plane defined by the fixed point. This relationship is established by the equation of a sphere, which includes the coordinates of the fixed point and accounts for the distance from the origin.

Related JEE Main Maths questions

• Consider the following two statements: Statement 1: If A, B and C are points with position vectors a = 2î + ĵ + k̂, b = 3î - ĵ + 3k̂ and c = î + 7ĵ - 5k̂, then the figure OABC forms a tetrahedron. Statement 2: If the position vectors a, b and c of points A, B and C are non-coplanar, then OABC is a tetrahedron, where O denotes the origin. Choose the correct option.
• The direction cosines l, m, n of one of the two lines satisfying the relations l - 5m + 3n = 0 and 7l² + 5m² - 3n² = 0 are
• A straight line is equally inclined to the x-axis and the y-axis, making an angle α with each. If its angle θ with the z-axis satisfies sin²θ = 2 sin²α, determine α.
• Let Q be the reflection of the point P(2, 3, 4) across the plane x − 2y + 5z = 6. The equation of the line joining P and Q is
• Find the point where the perpendicular drawn from the point (2, 4, −1) meets the line x + 5 = (1/4)(y + 3) = (−1/9)(z − 6).
• Find the equation of the plane that cuts the coordinate axes so as to form a triangle whose centroid is at (α, β, γ).

⚔️ Practice JEE Main Maths free + battle 1v1 →