JEE Mathematics

Equation of Plane: JEE Questions & Solutions

39 previous-year JEE Mathematics questions on Equation of Plane, each with a worked step-by-step solution.

Intermediate

Previous-year questions

  1. 01Let a point A lie between the parallel lines L₁ and L₂ such that its distances from L₁ and L₂ are 6 and 3 units, respectively. Then the…MCQMediumJEE 2026
  2. 02Let the plane containing the line of intersection of the planes P₁: x + (λ + 4)y + z = 1 and P₂: 2x + y + z = 2 pass through the points (0,…MCQMediumJEE 2023
  3. 03Let the equation of the plane passing through the line x - 2y - z - 5 = 0 and x + y + 3z - 5 = 0, and parallel to the line x + y + 2z - 7 =…NVAMediumJEE 2023
  4. 04Let the equation of the plane P containing the line x + 10 = (8 - y)/2 = z be ax + by + 3z = 2(a + b), and the distance of the plane P from…MCQMediumJEE 2023
  5. 05The plane 2x - y + z = 4 intersects the line segment joining the points A(a, -2, 4) and B(2, b, -3) at the point C in the ratio 2:1, and…MCQMediumJEE 2023
  6. 06Let a unit vector OP make angles α, β, γ with the positive directions of the coordinate axes OX, OY, OZ respectively, where β ∈ ( 0, π/2),…MCQMediumJEE 2023
  7. 07λ₁ < λ₂ are two values of λ such that the angle between the planes P₁: r · (3i - 5j + k) = 7 and P₂: r · (λ i + j - 3k) = 9 is sin⁻¹ (…NVAMediumJEE 2023
  8. 08If the equation of the plane passing through the point (1, 1, 2) and perpendicular to the line x - 3y + 2z - 1 = 0, 4x - y + z = 0 is Ax +…NVAMediumJEE 2023
  9. 09A vector v in the first octant is inclined to the x-axis at 60^°, to the y-axis at 45^° and to the z-axis at an acute angle. If a plane…MCQMediumJEE 2023
  10. 10If a plane passes through the points (-1, k, 0), (2, k, -1), (1, 1, 2) and is parallel to the line (x-1)/1 = (2y+1)/2 = (z+1)/(-1), then…MCQMediumJEE 2023
  11. 11Let θ be the angle between the planes P₁: r · ( i + j + 2 k) = 9 and P₂: r · (2 i - j + k) = 15. Let L be the line that meets P₂ at the…NVAEasyJEE 2023
  12. 12Let P be the plane, passing through the point (1, -1, -5) and perpendicular to the line joining the points (4, 1, -3) and (2, 4, 3). Then…MCQMediumJEE 2023
  13. 13Let the plane P: 8x + α₁ y + α₂ z + 12 = 0 be parallel to the line L: (x+2)/2 = (y-3)/3 = (z+4)/5. If the intercept of P on the y-axis is…MCQMediumJEE 2023
  14. 14The foot of perpendicular from the origin O to a plane P which meets the coordinate axes at the points A, B, C is (2, a, 4), a ∈ ℕ. If the…MCQMediumJEE 2023
  15. 15Let the image of the point P(2, -1, 3) in the plane x + 2y - z = 0 be Q. Then the distance of the plane 3x + 2y + z + 29 = 0 from the point…MCQMediumJEE 2023
  16. 16Let the plane P pass through the intersection of the planes 2x + 3y - z = 2 and x + 2y + 3z = 6, and be perpendicular to the plane 2x + y -…MCQMediumJEE 2023
  17. 17Let α x + β y + yz = 1 be the equation of a plane passing through the point (3, -2, 5) and perpendicular to the line joining the points (1,…NVAMediumJEE 2023
  18. 18If the equation of the plane passing through the line of intersection of the planes 2x - y + z = 3 and 4x - 3y + 5z + 9 = 0 and parallel to…MCQMediumJEE 2023
  19. 19Let the image of the point P(1, 2, 3) in the plane 2x - y + z = 9 be Q. If the coordinates of the point R are (6, 10, 7), then the square…NVAMediumJEE 2023
  20. 20A plane P contains the line of intersection of the plane r.(i+j+k) = 6 and r.(2i+3j+4k) = -5. If P passes through the point (0, 2, -2),…MCQMediumJEE 2023
  21. 21Let the line L pass through the point (0, 1, 2), intersect the line (x-1)/2 = (y-2)/3 = (z-3)/4 and be parallel to the plane 2x + y - 3z =…MCQMediumJEE 2023
  22. 22If the equation of the plane containing the line x + 2y + 3z - 4 = 0, 2x + y - z + 5 = 0, and perpendicular to the plane r = (i - j) + λ (i…MCQMediumJEE 2023
  23. 23Let λ₁, λ₂ be the values of λ for which the points (5/2, 1, λ) and (-2, 0, 1) are at equal distance from the plane 2x + 3y - 6z + 7 = 0. If…NVAMediumJEE 2023
  24. 24Let two vertices of a triangle ABC be (2, 4, 6) and (0,-2,-5), and its centroid be (2, 1,-1). If the image of the third vertex in the plane…MCQMediumJEE 2023
  25. 25Let P be the point of intersection of the line (x+3)/3 = (y+2)/1 = (1-z)/2 and the plane x + y + z = 2. If the distance of the point P from…MCQMediumJEE 2023
  26. 26Let time image of the point P(1, 2, 6) in the plane passing through the points A (1, 2, 0), B (1, 4, 1), and C (0, 5, 1) be Q(α, β, γ).…MCQMediumJEE 2023
  27. 27Let the line x/1 = (6 - y)/2 = (z + 8)/5 intersect the lines (x - 5)/4 = (y - 7)/3 = (z + 2)/1 and (x + 3)/6 = (3 - y)/3 = (z - 6)/1 at the…MCQMediumJEE 2023
  28. 28Let the foot of perpendicular from the point A(4, 3, 1) on the plane P: x - y + 2z + 3 = 0 be N. If B(5, α, β) is a point on plane P such…NVAMediumJEE 2023
  29. 29If equation of the plane that contains the point (-2, 3, 5) and is perpendicular to each of the planes 2x + 4y + 5z = 8 and 3x - 2y + 3z =…MCQMediumJEE 2023
  30. 30Let (α, β, γ) be the image of the point P(2, 3, 5) in the plane 2x + y - 3z = 6. Then α + β + γ is equal to:MCQMediumJEE 2023
  31. 31Let P be the plane passing through the points (5, 3, 0), (13, 3, -2), and (1, 6, 2). For α ∈ ℕ, if the distances of the points A(3, 4, α)…MCQMediumJEE 2023
  32. 32Let the line passing through the point P(2, -1, 2) and Q(5, 3, 4) meet the plane x - y + z = 4 at the point T. Then the distance of the…MCQMediumJEE 2023
  33. 33Let the line ℓ: x = (1 - y)/(-2) = (z - 3)/λ, λ ∈ ℝ meet the plane P: x + 2y + 3z = 4 at the point (α, β, γ). If the angle between the line…NVAMediumJEE 2023
  34. 34Let the plane P: 4x - y + z = 10 be rotated by an angle π/2 about its line of intersection with the plane x + y - z = 4. If α is the…MCQMediumJEE 2023
  35. 35Let the plane x + 3y - 2z + 6 = 0 meet the co-ordinate axes at the points A, B, C. If the orthocentre of the triangle ABC is (α, β, 6/7),…NVAMediumJEE 2023
  36. 36The plane, passing through the points (0, -1, 2) and (-1, 2, 1) and parallel to the line passing through (5,1,-7) and (1,-1,-1), also…MCQMediumJEE 2023
  37. 37Let N be the foot of perpendicular from the point P(1, -2, 3) on the line passing through the points (4, 5, 8) and (1, -7, 5). Then the…MCQMediumJEE 2023
  38. 38Let the foot of the perpendicular of the point P(3,-2,-9) on the plane passing through the points (-1,-2,-3), (9,3,4), (9,-2,1) be…MCQMediumJEE 2023
  39. 39Let the plane P contain the line 2x+y-z-3=0=5x-3y+4z+9 and be parallel to the line (x+2)/2=(3-y)/(-4)=(z-7)/5. Then the distance of the…NVAHardJEE 2023

Frequently asked questions

Our bank has 39 previous-year JEE Mathematics questions tagged to Equation of Plane, drawn from JEE papers between 2023 and 2026, including 1 from 2026 alone. Each comes with a full step-by-step solution.

Equation of Plane is rated Intermediate overall for JEE Mathematics. The PYQs on this page break down as 37 medium, 1 easy, 1 hard.

Of the 39 previous-year questions on Equation of Plane, 28 are multiple-choice (MCQ) and 11 are numerical-value (NVA) questions.

Based on recent paper analysis, Equation of Plane is worth about 2 marks in JEE Main. It sits in Three-Dimensional Geometry, a Class 12 Mathematics chapter.

More Three-Dimensional Geometry topics

Equation of Line in 3D57Skew Lines & Shortest Distance26Coordinates in 3D6Direction Cosines & Ratios3

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