Exams › JEE Main › Maths

Find the equation of the line lying in the plane π: 2x - y + z - 4 = 0, perpendicular to the line (x-2)/(1) = (y-2)/(-1) = (z-3)/(-2), and passing through the point where this line meets π.

1. (x-2)/(3) = (y-1)/(5) = (z-1)/(-1)
2. (x-1)/(3) = (y-3)/(5) = (z-5)/(-1)
3. (x+2)/(2) = (y+1)/(-1) = (z+1)/(1)
4. (x-2)/(2) = (y-1)/(-1) = (z-1)/(1)

Correct answer: (x-1)/(3) = (y-3)/(5) = (z-5)/(-1)

Solution

The given line meets the plane at (1,3,5). The required line lies in the plane and is perpendicular to the given line, so its direction is n_plane x d_line = (2,-1,1)x(1,-1,-2)=(3,5,-1). The line is (x-1)/3=(y-3)/5=(z-5)/(-1).

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 →