Q. Calculate the distance from the point (1, 2, 3) to the origin (0, 0, 0). (2021)
A.
√14
B.
√6
C.
√9
D.
√12
Show solution
Solution
Distance = √[(1-0)² + (2-0)² + (3-0)²] = √[1 + 4 + 9] = √14.
Correct Answer:
A
— √14
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Q. Calculate the distance from the point P(1, 2, 3) to the origin O(0, 0, 0). (2023)
Show solution
Solution
Distance = √[(1-0)² + (2-0)² + (3-0)²] = √[1 + 4 + 9] = √14.
Correct Answer:
B
— √14
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Q. Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(6, 0, 0), and C(0, 8, 0). (2023)
A.
(2, 2, 0)
B.
(2, 3, 0)
C.
(3, 2, 0)
D.
(0, 0, 0)
Show solution
Solution
Centroid = ((0+6+0)/3, (0+0+8)/3, (0+0+0)/3) = (2, 2.67, 0).
Correct Answer:
A
— (2, 2, 0)
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Q. Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(0, 4, 0), and C(3, 0, 0). (2021)
A.
(1, 1.33, 0)
B.
(1, 2, 0)
C.
(0, 1.33, 0)
D.
(0, 2, 0)
Show solution
Solution
Centroid = ((0+0+3)/3, (0+4+0)/3, (0+0+0)/3) = (1, 1.33, 0).
Correct Answer:
B
— (1, 2, 0)
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Q. Determine the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2023)
A.
(1, 1, 0)
B.
(2, 1, 0)
C.
(4/3, 1, 0)
D.
(0, 1, 0)
Show solution
Solution
Centroid G = ((0+4+0)/3, (0+0+3)/3, (0+0+0)/3) = (4/3, 1, 0).
Correct Answer:
B
— (2, 1, 0)
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Q. Determine the coordinates of the centroid of the triangle with vertices A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2021)
A.
(4, 5, 6)
B.
(3, 4, 5)
C.
(5, 6, 7)
D.
(6, 7, 8)
Show solution
Solution
Centroid G = ((1+4+7)/3, (2+5+8)/3, (3+6+9)/3) = (4, 5, 6).
Correct Answer:
B
— (3, 4, 5)
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Q. Determine the coordinates of the foot of the perpendicular from the point (1, 2, 3) to the plane x + 2y + 3z = 14. (2023)
A.
(2, 3, 4)
B.
(1, 2, 4)
C.
(2, 1, 3)
D.
(3, 2, 1)
Show solution
Solution
Using the formula for the foot of the perpendicular, we find the coordinates to be (1, 2, 4).
Correct Answer:
B
— (1, 2, 4)
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Q. Find the area of a triangle with vertices at A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)
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Solution
Area = 0.5 * base * height = 0.5 * 1 * 1 = 0.5 square units.
Correct Answer:
A
— 0.5
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Q. Find the area of the triangle formed by the points A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)
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Solution
Area = 0.5 * base * height = 0.5 * 1 * 1 = 0.5 square units.
Correct Answer:
A
— 0.5
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Q. Find the area of the triangle formed by the points A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9). (2022)
Show solution
Solution
The points are collinear, hence the area = 0.
Correct Answer:
A
— 0
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Q. Find the coordinates of the centroid of the triangle with vertices A(0, 0, 0), B(4, 0, 0), C(0, 3, 0). (2021)
A.
(4/3, 1, 0)
B.
(2, 1, 0)
C.
(1, 1, 0)
D.
(0, 0, 0)
Show solution
Solution
Centroid G = ((0+4+0)/3, (0+0+3)/3, (0+0+0)/3) = (4/3, 1, 0).
Correct Answer:
B
— (2, 1, 0)
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Q. Find the coordinates of the midpoint of the line segment joining A(2, -1, 3) and B(4, 3, 5). (2022)
A.
(3, 1, 4)
B.
(2, 1, 4)
C.
(3, 2, 3)
D.
(4, 2, 4)
Show solution
Solution
Midpoint M = ((2+4)/2, (-1+3)/2, (3+5)/2) = (3, 1, 4).
Correct Answer:
A
— (3, 1, 4)
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Q. Find the coordinates of the midpoint of the line segment joining A(2, 3, 4) and B(4, 5, 6). (2023)
A.
(3, 4, 5)
B.
(2, 3, 4)
C.
(4, 5, 6)
D.
(5, 6, 7)
Show solution
Solution
Midpoint M = ((2+4)/2, (3+5)/2, (4+6)/2) = (3, 4, 5).
Correct Answer:
A
— (3, 4, 5)
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Q. Find the distance between the parallel planes 2x + 3y + 4z = 5 and 2x + 3y + 4z = 10. (2023)
A.
5/√29
B.
10/√29
C.
15/√29
D.
20/√29
Show solution
Solution
Distance = |d1 - d2| / √(a² + b² + c²) = |5 - 10| / √(2² + 3² + 4²) = 5 / √29.
Correct Answer:
B
— 10/√29
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Q. Find the distance between the parallel planes 2x + 3y + z = 5 and 2x + 3y + z = 10. (2022)
Show solution
Solution
Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + 1²) = 5 / √14.
Correct Answer:
A
— 5
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Q. Find the distance between the parallel planes x + 2y + 3z = 4 and x + 2y + 3z = 10. (2023)
Show solution
Solution
Distance = |d1 - d2| / √(a² + b² + c²) = |4 - 10| / √(1² + 2² + 3²) = 6 / √14.
Correct Answer:
A
— 2
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Q. Find the length of the diagonal of a cuboid with dimensions 3, 4, and 12 units. (2020)
A.
√169
B.
√145
C.
√153
D.
√157
Show solution
Solution
Diagonal = √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13.
Correct Answer:
C
— √153
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Q. Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6 units. (2022)
A.
√49
B.
√45
C.
√36
D.
√50
Show solution
Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7 units.
Correct Answer:
A
— √49
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Q. Find the length of the diagonal of a rectangular box with dimensions 2, 3, and 6. (2023)
A.
√49
B.
√36
C.
√45
D.
√50
Show solution
Solution
Diagonal = √(2² + 3² + 6²) = √(4 + 9 + 36) = √49 = 7.
Correct Answer:
A
— √49
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Q. If the coordinates of a point P are (1, -1, 2), what is the x-coordinate of the point Q if it is reflected across the yz-plane? (2023)
Show solution
Solution
Reflection across the yz-plane changes the sign of the x-coordinate. So, Q = (-1, -1, 2).
Correct Answer:
B
— -1
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Q. What is the area of a triangle with vertices at A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0)? (2022)
Show solution
Solution
Area = 0.5 * base * height = 0.5 * 1 * 1 = 0.5 square units.
Correct Answer:
A
— 0.5
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Q. What is the area of the base of a cone with radius 3? (2023)
Show solution
Solution
Area of base = πr² = π(3²) = 9π square units.
Correct Answer:
A
— 9π
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Q. What is the area of the base of a cylinder with radius 4 units? (2020)
A.
16π
B.
8π
C.
12π
D.
20π
Show solution
Solution
Area of base = πr² = π(4)² = 16π square units.
Correct Answer:
A
— 16π
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Q. What is the distance between the parallel planes 2x + 3y - z = 5 and 2x + 3y - z = 10? (2021)
A.
5/√14
B.
10/√14
C.
15/√14
D.
20/√14
Show solution
Solution
Distance = |d1 - d2| / √(A² + B² + C²) = |5 - 10| / √(2² + 3² + (-1)²) = 5/√14.
Correct Answer:
B
— 10/√14
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Q. What is the distance between the parallel planes x + 2y + 3z = 4 and x + 2y + 3z = 10? (2023)
Show solution
Solution
Distance = |d1 - d2| / √(a² + b² + c²) = |4 - 10| / √(1² + 2² + 3²) = 6 / √14.
Correct Answer:
A
— 2
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Q. What is the distance between the point (2, 3, 4) and the plane x + y + z = 10? (2022)
Show solution
Solution
Distance = |(2 + 3 + 4 - 10) / √(1² + 1² + 1²)| = |(-1)/√3| = 1/√3.
Correct Answer:
A
— 1
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Q. What is the distance between the points A(1, 2, 3) and B(4, 5, 6)? (2023)
A.
3√2
B.
3√3
C.
3
D.
√27
Show solution
Solution
Distance = √[(4-1)² + (5-2)² + (6-3)²] = √[3² + 3² + 3²] = √27 = 3√3.
Correct Answer:
A
— 3√2
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Q. What is the equation of a plane passing through the point (1, 2, 3) with normal vector (1, 1, 1)? (2022)
A.
x + y + z = 6
B.
x + y + z = 3
C.
x + y + z = 1
D.
x + y + z = 0
Show solution
Solution
Equation of the plane: 1(x-1) + 1(y-2) + 1(z-3) = 0 => x + y + z = 6.
Correct Answer:
A
— x + y + z = 6
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Q. What is the equation of a plane passing through the point (1, 2, 3) with normal vector (2, -1, 3)? (2021)
A.
2x - y + 3z = 12
B.
2x + y - 3z = 0
C.
2x - y + 3z = 0
D.
2x + y + 3z = 12
Show solution
Solution
Equation of the plane: 2(x-1) - 1(y-2) + 3(z-3) = 0 simplifies to 2x - y + 3z = 12.
Correct Answer:
C
— 2x - y + 3z = 0
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Q. What is the equation of the plane passing through the point (1, 2, 3) with normal vector (1, -1, 1)? (2023)
A.
x - y + z = 0
B.
x + y + z = 6
C.
x - y + z = 1
D.
x + y - z = 0
Show solution
Solution
Equation of the plane: 1(x-1) - 1(y-2) + 1(z-3) = 0 => x - y + z = 1.
Correct Answer:
C
— x - y + z = 1
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Showing 1 to 30 of 37 (2 Pages)
3D Geometry MCQ & Objective Questions
Understanding 3D Geometry is crucial for students preparing for school and competitive exams. This branch of mathematics deals with the properties and relationships of three-dimensional shapes, making it essential for various subjects. Practicing MCQs and objective questions in 3D Geometry not only enhances conceptual clarity but also boosts confidence, helping students score better in their exams.
What You Will Practise Here
Key concepts of 3D shapes such as cubes, spheres, and cylinders.
Formulas for surface area and volume of three-dimensional figures.
Understanding coordinates in three-dimensional space.
Diagrams and visual representations of 3D objects.
Applications of 3D Geometry in real-life scenarios.
Common theorems related to 3D Geometry.
Problem-solving techniques for 3D Geometry MCQs.
Exam Relevance
3D Geometry is a significant topic in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that require them to apply formulas, interpret diagrams, and solve problems related to three-dimensional shapes. Common question patterns include calculating volumes, determining surface areas, and solving real-world problems using 3D Geometry concepts.
Common Mistakes Students Make
Confusing the formulas for surface area and volume.
Misinterpreting the dimensions of 3D shapes in diagrams.
Overlooking the importance of units in calculations.
Failing to visualize the 3D objects while solving problems.
FAQs
Question: What are some important 3D Geometry MCQ questions for exams?Answer: Important questions often include calculating the volume of a sphere or the surface area of a cube, as these concepts are frequently tested.
Question: How can I improve my understanding of 3D Geometry?Answer: Regular practice of 3D Geometry objective questions with answers can significantly enhance your understanding and retention of the concepts.
Don't wait any longer! Start solving practice MCQs on 3D Geometry today to test your understanding and prepare effectively for your exams. Your success is just a question away!
