Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry – Extra Questions with Answers

Moving from two dimensions to three means trading four quadrants for eight octants and adding a z-axis to the coordinate system. These Class 11 Maths Chapter 11 questions check the distance formula and basic coordinate concepts in 3D space.

Last Updated: September 23, 2026

Very Short Answer Questions (1 mark)

Q1. How many coordinate planes are there in 3D space?
Ans: 3 (xy-plane, yz-plane, zx-plane).

Q2. Write the coordinates of the origin in 3D.
Ans: (0,0,0).

Q3. Find the distance between (0,0,0) and (1,2,2).
Ans: √(1+4+4) = √9 = 3.

Q4. On which axis does a point (0,0,z) lie?
Ans: The z-axis.

Q5. How many quadrants exist in 2D, and how many octants in 3D?
Ans: 4 quadrants in 2D; 8 octants in 3D.

Short Answer Questions (2–3 marks)

Q6. Find the distance between the points (1,2,3) and (4,6,3).
Ans: √[(4−1)²+(6−2)²+(3−3)²] = √[9+16+0] = √25 = 5.

Q7. Find the midpoint of the line segment joining (2,4,6) and (4,8,10) using the section formula (ratio 1:1).
Ans: Midpoint = [(2+4)/2, (4+8)/2, (6+10)/2] = (3, 6, 8).

Q8. Explain how the 3D distance formula is a natural extension of the 2D (Pythagoras-based) distance formula.
Ans: The 2D distance formula, √[(x2−x1)²+(y2−y1)²], comes from applying the Pythagoras theorem to the horizontal and vertical differences between two points. In 3D, an additional dimension (z) is added, and applying the Pythagoras theorem principle again (essentially twice, once in a plane and once out of it) gives the extended formula with a third squared-difference term added under the square root.

Higher-Order Thinking / Application Questions

Q9. A drone is positioned at coordinates (2,3,10) (with z representing height above ground), and needs to fly to a charging station at (8,3,0). Find the straight-line distance it must travel, and explain what the z-coordinate difference represents physically.
Ans: Distance = √[(8−2)²+(3−3)²+(0−10)²] = √[36+0+100] = √136 ≈ 11.66 units. The z-coordinate difference (10−0=10) represents the vertical drop in height the drone must descend as part of its straight-line path to the ground-level charging station.

Q10. Three points A(1,1,1), B(3,3,3), and C(2,2,2) are given. Using the distance formula, determine whether C lies exactly on the line segment AB (i.e., is the midpoint), and justify your answer with a calculation.
Ans: Using the midpoint (section formula with ratio 1:1) of A and B: [(1+3)/2, (1+3)/2, (1+3)/2] = (2,2,2), which exactly matches point C. This confirms C is indeed the midpoint of segment AB, lying exactly on the line between them.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

How would you find the distance between the points (1,2,3) and (4,6,3) in space?
Using the distance formula, root of (3 squared + 4 squared + 0 squared) = root(9+16) = 5 units.

What are the coordinates of the point dividing the segment joining (1,2,3) and (5,6,7) in ratio 1:3 internally?
Using the section formula, the point is ((1×5+3×1)/4, (1×6+3×2)/4, (1×7+3×3)/4) = (2,3,4).

Written by Satish

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