Introduction to Three Dimensional Geometry Case Study Questions Class 11 Maths Chapter 11

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Hello students, we are providing case study questions for class 11 Maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 11 Maths. In this article, you will find case study questions for cbse class 11 Maths chapter 11 Introduction to Three Dimensional Geometry.

Chapter	Introduction to Three Dimensional Geometry
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	11
Subject	Maths
Useful for	Class 12 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 11 Maths Chapterwise Case Study

Table of Contents

Case Study Questions on Introduction to Three Dimensional Geometry

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Case Study:
A drone survey company is mapping part of a field. They use three landmark posts located at points \( A(2, -1, 3) \), \( B(4, 3, 5) \), and \( C(6, 0, 4) \) for their 3D mapping work. Precise coordinates are needed to determine distances, midpoints, and relationships among these sites.

Questions:

Find the distance between points \( A \) and \( B \). Write the answer in exact and decimal form.
Calculate the coordinates of the midpoint \( M \) of segment \( BC \).
Check whether the points \( A \), \( B \), and \( C \) are collinear.
If another observation station must be set up such that its position vector is the average of \( \vec{OA} \), \( \vec{OB} \), and \( \vec{OC} \), find its coordinates and interpret the meaning.

Solutions:

1. Distance between \( A(2, -1, 3) \) and \( B(4, 3, 5) \):

\[ AB = \sqrt{(4 – 2)^2 + (3 – (-1))^2 + (5 – 3)^2} = \sqrt{2^2 + 4^2 + 2^2} = \sqrt{4 + 16 + 4} = \sqrt{24} = 2\sqrt{6} \approx 4.90\ \text{units} \]

2. Midpoint \( M \) of \( BC \):

Midpoint formula: \[ M = \left( \frac{4 + 6}{2}, \frac{3 + 0}{2}, \frac{5 + 4}{2} \right) = (5, 1.5, 4.5) \]

3. Are points \( A, B, C \) collinear?

Compute direction ratios for \( \vec{AB} \) and \( \vec{BC} \): \[ \vec{AB} = (4-2,\ 3-(-1),\ 5-3) = (2, 4, 2) \] \[ \vec{BC} = (6-4,\ 0-3,\ 4-5) = (2, -3, -1) \] If \( A, B, C \) are collinear, then \( \vec{AB} \) and \( \vec{BC} \) are proportional: \[ \frac{2}{2} = 1,\quad \frac{4}{-3} = -\frac{4}{3},\quad \frac{2}{-1} = -2 \] All ratios are not equal. \[ \boxed{\text{No, points } A, B, C \text{ are not collinear.}} \]

4. Observation station at average position vector:

Position vector \( \vec{OP} = \frac{1}{3} (\vec{OA} + \vec{OB} + \vec{OC}) \): \[ = \left( \frac{2 + 4 + 6}{3},\ \frac{-1 + 3 + 0}{3},\ \frac{3 + 5 + 4}{3} \right) = (4, \frac{2}{3}, 4) \] So, the required coordinates are \( (4,\ \frac{2}{3},\ 4) \). \textbf{Interpretation:} This point is the centroid (average location) of the triangle formed by \( A, B, C \) — useful as a central base or reference for survey work.

We hope the given case study questions for Introduction to Three Dimensional Geometry Class 11 helps you in your learning.

Also check

Topics from which case study questions may be asked

Introduction to 3D Geometry
Coordinate Axes and Coordinate Planes in Three Dimensions
Coordinates of a Point in Space
Distance Between Two Points in 3D
Section Formula in 3D
Direction Cosines and Direction Ratios (brief introduction, if included)

Frequently Asked Questions (FAQs) on Introduction to Three Dimensional Geometry Case Study Questions

Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:
Read the problem carefully: Understand the scenario and identify the mathematical concepts involved.
Break down the problem: Divide the case study into smaller parts to manage the information better.
Apply relevant formulas and theorems: Use the appropriate mathematical tools to solve each part of the problem.

Q3: Why are case study questions included in the Class 11 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

Q4: Are there any online resources or tools available for practicing “Introduction to Three Dimensional Geometry” case study questions?

A12: We provide case study questions for CBSE Class 11 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.