JEE (Main) Mathematics - THREE DIMENSIONAL GEOMETRY Multiple Choice Questions (MCQs)
JEE (Main) Mathematics - Three Dimensional Geometry MCQs
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What are the coordinates of a point in 3D space?
- A) (x, y)
- B) (x, y, z)
- C) (x, z)
- D) (y, z)
Answer: B) (x, y, z)
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The distance between the points A(1, 2, 3) and B(4, 5, 6) is:
- A) √27
- B) √14
- C) √12
- D) √22
Answer: A) √27
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What is the formula for the distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂)?
- A) √[(x₂ - x₁)² + (y₂ - y₁)²]
- B) √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
- C) √[(x₁ - x₂)² + (y₁ - y₂)² + (z₁ - z₂)²]
- D) √[(x₁ - x₂)² + (y₁ - y₂)²]
Answer: B) √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
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The distance between points A(1, 0, 0) and B(4, 3, 0) is:
- A) 5
- B) 6
- C) √17
- D) √13
Answer: A) 5
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The distance between points P(-3, -1, 2) and Q(1, 3, -4) is:
- A) 10
- B) √56
- C) 8
- D) √64
Answer: B) √56
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Which of the following is the correct formula for finding the distance between two points on a 3D plane?
- A) d = √[(x₂ - x₁)² + (y₂ - y₁)²]
- B) d = √[(x₂ - x₁)² + (z₂ - z₁)²]
- C) d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
- D) d = √[(y₂ - y₁)² + (z₂ - z₁)²]
Answer: C) d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
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What is the distance between the points A(2, -1, 3) and B(2, -1, -3)?
- A) 6
- B) 0
- C) 3
- D) 4
Answer: C) 3
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If the coordinates of two points are P(1, 2, 3) and Q(4, 5, 6), then the distance between them is:
- A) 3√3
- B) √27
- C) √19
- D) 6
Answer: B) √27
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The distance between the points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) is 10 units. What is the correct equation?
- A) (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² = 100
- B) (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² = 10
- C) (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² = 50
- D) None of the above
Answer: A) (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² = 100
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If A(2, 3, 1) and B(1, -1, 4) are two points, then the distance between them is:
- A) √19
- B) √12
- C) √14
- D) √18
Answer: A) √19
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The coordinates of a point in space can be represented as:
- A) Two values (x, y)
- B) Three values (x, y, z)
- C) One value (x)
- D) None of the above
Answer: B) Three values (x, y, z)
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The distance between points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) is 10 units. What is the correct equation?
- A) (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² = 100
- B) (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² = 10
- C) (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² = 50
- D) None of the above
Answer: A) (x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² = 100
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The distance between the point (x, y, z) and the origin (0, 0, 0) is:
- A) √(x² + y²)
- B) √(x² + y² + z²)
- C) x + y + z
- D) √(x² + z²)
Answer: B) √(x² + y² + z²)
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If the distance between points P(1, 0, 0) and Q(4, 3, 0) is 5, then the coordinates of P and Q lie on:
- A) The x-axis
- B) The y-axis
- C) The z-axis
- D) A plane parallel to the x-y plane
Answer: D) A plane parallel to the x-y plane
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The distance between the points P(2, -1, 3) and Q(2, 5, -3) is:
- A) √56
- B) √65
- C) 6
- D) 8
Answer: B) √65
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