JEE Main Mathematics: Distance between two points in 3D Practice Questions
6 free multiple-choice questions on Distance between two points in 3D (Analytical Geometry) for JEE Main Mathematics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more JEE Main questions in the app →Q1. If two points are (1, 1, 1) and (1, 1, 5), what is the distance between them?
Show answer & explanation
Correct answer: A — 3
Distance D = √((1-1)² + (1-1)² + (5-1)²) = √(0² + 0² + 4²) = √16 = 4.
Q2. If two points are A(x₁, y₁, z₁) and B(x₂, y₂, z₂), the distance between them is given by which formula?
Show answer & explanation
Correct answer: D — √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²)
The distance D between two points in 3D space is found by taking the square root of the sum of the squares of the differences in their corresponding coordinates: D = √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²).
Q3. Find the distance between the points P(5, 0, 0) and Q(5, 0, 12).
Show answer & explanation
Correct answer: A — 12
Since the x and y coordinates are the same, the distance is simply the absolute difference in the z-coordinate: D = √((5-5)² + (0-0)² + (12-0)²) = √144 = 12.
Q4. If the distance between two points in 3D space is 5 units, what is the square of that distance?
Show answer & explanation
Correct answer: D — 25
If the distance D=5, then the square of the distance is D² = 5² = 25.
Q5. What is the distance between the points P(0, 0, 0) and Q(a, b, c) in 3D space?
Show answer & explanation
Correct answer: A — √(a²+b²+c²)
The distance between the origin (0, 0, 0) and any point (a, b, c) is simply the magnitude of the position vector, which is calculated as √(a² + b² + c²).
Q6. The distance between the points (0, 0, 0) and (3, 4, 0) is given by which formula?
Show answer & explanation
Correct answer: B — 5
The distance formula is D = √((3-0)² + (4-0)² + (0-0)²) = √(3² + 4² + 0²) = √(9 + 16) = √25 = 5.
Keep going — practice on Padhai Karlo
Padhai Karlo gives you unlimited JEE Main practice: chapter-wise questions, timed quizzes, and full mock tests with an All-India Rank — free to start.
Get the free Android app →