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3D Geometry & Planes
JEE Mathematics • 10 questions • Free on ExamBattle
Practice Questions
Q1
Direction cosines of a vector satisfy:
- A. l + m + n = 1
- B. l² + m² + n² = 1
- C. lmn = 1
- D. l = m = n
Q2
The equation of a plane passing through (a, b, c) with normal (p, q, r) is:
- A. ax + by + cz = 0
- B. p(x-a) + q(y-b) + r(z-c) = 0
- C. ax + by + cz = 1
- D. x + y + z = a + b + c
Q3
The distance between parallel planes x + 2y + 3z = 4 and x + 2y + 3z = 8 is:
- A. 4/√14
- B. 4
- C. 8/√14
- D. √14
Q4
The angle between two planes with normals n₁ and n₂ is θ where cosθ = ?
- A. (n₁·n₂)/(|n₁||n₂|)
- B. (n₁×n₂)/(|n₁||n₂|)
- C. |n₁-n₂|
- D. |n₁|+|n₂|
Q5
The distance from point (1, 2, 3) to plane 2x + 3y + 6z = 14 is:
- A. 1
- B. 2
- C. 3
- D. √14
Q6
The equation of line passing through (1, 0, 2) with direction (2, 3, -1) is:
- A. (x-1)/2 = (y-0)/3 = (z-2)/(-1)
- B. (x-1)/3 = (y-0)/2 = (z-2)/(-1)
- C. (x-1)/2 = (y-3)/0 = (z-2)/(-1)
- D. x + 3y - z = 1
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