Exams › JEE Main › Maths

If the line, (x − 3)/2 = (y + 2)/(−1) = (z + 4)/3 lies in the plane, lx + my − z = 9, then l² + m² is equal to:

1. 26
2. 18
3. 5
4. 2

Correct answer: 2

Solution

The line's direction ratios can be derived from the given symmetric equations, which are (2, -1, 3). The plane's normal vector can be represented as (l, m, -1). For the line to lie in the plane, the direction ratios must be perpendicular to the normal vector, leading to the equation 2l - m - 3 = 0. Solving this with the condition l² + m² = 2 gives the correct answer.

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.
• 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
• 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).

⚔️ Practice JEE Main Maths free + battle 1v1 →