Introduction to Three Dimensional Geometry Practice Questions
Class 11 · Mathematics · 851 free MCQs with instant results and detailed explanations.
851
Total
324
Easy
404
Medium
123
Hard
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Topics in Introduction to Three Dimensional Geometry
Coordinate Axes
524
Section Formula
140
Distance Formula
187
Sample Questions from Introduction to Three Dimensional Geometry
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
What is the distance between the points A(1, 2, 3) and B(4, 5, 6) in 3D space?
A.
5.196
B.
3
C.
2.236
D.
7
Show Answer & Explanation
Correct Answer: A
The distance formula in 3D is √[(x2-x1)² + (y2-y1)² + (z2-z1)²]. Substituting the coordinates gives √[(4-1)² + (5-2)² + (6-3)²] = √[9 + 9 + 9] = √27 = 5.196.
Q2
Easy
How do you represent the equation of a plane in 3D space?
A.
Ax + By + Cz + D = 0
B.
x² + y² + z² = r²
C.
y = mx + c
D.
x + y + z = 1
Show Answer & Explanation
Correct Answer: A
The general equation of a plane in three-dimensional space is given by Ax + By + Cz + D = 0, where A, B, C are the coefficients.
Q3
Easy
Which of the following points lies on the x-axis in 3D coordinates?
A.
(0, 1, 0)
B.
(3, 0, 0)
C.
(0, 0, 4)
D.
(1, 1, 1)
Show Answer & Explanation
Correct Answer: B
A point lies on the x-axis if its y and z coordinates are both zero. Here, (3, 0, 0) satisfies this condition.
Q4
Medium
In a 3D coordinate system, which of the following is true for the point (0, 0, 0)?
A.
It is the origin.
B.
It represents a unit vector.
C.
It is on the x-axis.
D.
It indicates a negative coordinate.
Show Answer & Explanation
Correct Answer: A
The point (0, 0, 0) is defined as the origin in a three-dimensional coordinate system.
Q5
Medium
The coordinates of the midpoint M of a line segment joining points A(1, 2, 3) and B(4, 5, 6) are given by which formula?
A.
((x1+x2)/2, (y1+y2)/2, (z1+z2)/2)
B.
(x1+x2, y1+y2, z1+z2)
C.
((x1-x2)/2, (y1-y2)/2, (z1-z2)/2)
D.
(x1, y1, z1)
Show Answer & Explanation
Correct Answer: A
The midpoint M is calculated as the average of the coordinates of points A and B.
Q6
Medium
Which of the following sets of coordinates represents a point in the positive octant of 3D space?
A.
(2, 3, -1)
B.
(0, 1, 5)
C.
(1, 1, 1)
D.
(-1, 0, 0)
Show Answer & Explanation
Correct Answer: C
The positive octant in 3D space is characterized by all coordinates being positive.
Q7
Medium
Which coordinate system uses three numbers to specify a point's position based on its distance from three axes?
A.
Cartesian
B.
Polar
C.
Spherical
D.
Cylindrical
Show Answer & Explanation
Correct Answer: A
The Cartesian coordinate system uses three values to represent a point using its distances from the x, y, and z axes.
Q8
Hard
In which quadrant does the point (−3, −2, 4) lie in 3D space?
A.
All positive quadrants
B.
First quadrant
C.
Third quadrant
D.
None of the quadrants
Show Answer & Explanation
Correct Answer: D
In 3D space, points are classified based on all three coordinates. Since x and y are negative, but z is positive, it does not belong to any single quadrant.
Q9
Hard
What is the equation of the plane passing through the points (1, 2, 3), (4, 5, 6), and (7, 8, 9)?
A.
x + y + z = 12
B.
x + 2y + 3z = 12
C.
x + y + z = 1
D.
No plane can pass through these points
Show Answer & Explanation
Correct Answer: D
The three points are collinear (they lie on the same line), hence there is no unique plane that can be defined through them.
Q10
Hard
Given a point P(2, 3, 1), determine the equation of the line passing through this point and parallel to the vector v = (1, -1, 2).
A.
(x-2)/1 = (y-3)/-1 = (z-1)/2
B.
(x-2)/2 = (y-3)/1 = (z-1)/-1
C.
(x-2)/1 = (y-3)/1 = (z-1)/-2
D.
(x-2)/-1 = (y-3)/2 = (z-1)/1
Show Answer & Explanation
Correct Answer: A
The parametric equations for a line can be formulated as (x-x0)/a = (y-y0)/b = (z-z0)/c, where (a, b, c) are direction ratios. Here, it becomes (x-2)/1 = (y-3)/-1 = (z-1)/2.
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Introduction to Three Dimensional Geometry — Class 11 Mathematics Practice Questions Online
This page contains 851 practice MCQs for the chapter Introduction to Three Dimensional Geometry in Class 11 Mathematics. The questions are organized by difficulty — 324 easy, 404 medium, 123 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.