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Important Questions

Introduction to Three Dimensional Geometry

ICSE · Class 11 · Mathematics

Most important questions from Introduction to Three Dimensional Geometry for ICSE Class 11 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

59 questions30 flashcards5 concepts

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A basic representation of the three-dimensional Cartesian coordinate system showing the X, Y, and Z axes intersecting at the origin.
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59 Questions·
multiple choice

Sample Questions

1multiple choice
3 marks

Find the point on the x-axis that is equidistant from A(1, 2, 2) and B(7, 5, 8).

Show answer

(11/2, 0, 0)

Let the point be P(x, 0, 0). Then PA = PB. So √((x-1)^2 + (0-2)^2 + (0-2)^2) = √((x-7)^2 + (0-5)^2 + (0-8)^2). Squaring gives (x-1)^2 + 8 = (x-7)^2 + 89. Simplifying: x^2 - 2x + 9 = x^2 - 14x + 138, so 12x = 129 and x = 11/2. Therefore P = (11/2, 0, 0).

2multiple choice
3 marks

A point lies in the yz-plane and is equidistant from A(2, 0, 3), B(0, 3, 2) and C(0, 0, 1). Find the point.

Show answer

(0, 1, 3)

Let P = (0, y, z). Equating PA and PB gives 3y - z = 0. Equating PB and PC gives 3y + z = 6. Solving these two equations gives y = 1 and z = 3. So the point is (0, 1, 3).

3multiple choice
3 marks

Find the coordinates of the centroid of triangle with vertices A(1, 2, 3), B(4, 5, 6) and C(7, 8, 9).

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(4, 5, 6)

The centroid is the average of the three vertices. So G = ((1+4+7)/3, (2+5+8)/3, (3+6+9)/3) = (4, 5, 6).

4multiple choice
3 marks

Find the coordinates of the point that divides the line segment joining P(2, -3, 4) and Q(8, 0, 10) in the ratio 1:2 internally.

Show answer

(4, -2, 6)

Use the internal section formula with m:n = 1:2. Coordinates are ((1·8 + 2·2)/3, (1·0 + 2·(-3))/3, (1·10 + 2·4)/3) = (4, -2, 6).

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Frequently Asked Questions

What are the important topics in Introduction to Three Dimensional Geometry for ICSE Class 11 Mathematics?
Key topics in Introduction to Three Dimensional Geometry include Three Dimensional Geometry Concept Map, Three Dimensional Geometry Concept Map, Three Dimensional Geometry Concept Map. These are the concepts ICSE Class 11 examiners draw on most — study them first, then practise related questions.
How to score full marks in Introduction to Three Dimensional Geometry — ICSE Class 11 Mathematics?
Understand the core concepts first, then work through the 59 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Introduction to Three Dimensional Geometry?
There are 59 practice questions available for Introduction to Three Dimensional Geometry. These cover multiple question types including MCQs, short answer, and long answer questions.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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