Vectors Case Study Questions Class 12 Maths Chapter 10

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Hello students, we are providing case study questions for class Class 12 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 Class 12 Maths. In this article, you will find case study questions for cbse class Class 12 Maths chapter 10 Vectors.

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

Table of Contents

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Case Study Questions on Vectors

Case Study:
A rescue team has to deliver relief material to a location at point \( B \) by traveling from their base at point \( A \), then heading to a check post at point \( C \) before returning to base. The coordinates of the points are:

Base: \( A(1,\, 2,\, 3) \)
Relief location: \( B(4,\, 6,\, 8) \)
Check post: \( C(2,\, 4,\, 5) \)

Questions:

Find the vector \( \vec{AB} \) and \( \vec{BC} \).
Calculate the total distance the team covers if they travel from \( A \) to \( B \), then to \( C \), and finally back to \( A \).
Find the angle between vectors \( \vec{AB} \) and \( \vec{BC} \).

Solutions:

1. Vectors \( \vec{AB} \) and \( \vec{BC} \):

\[ \vec{AB} = \langle 4-1,\, 6-2,\, 8-3 \rangle = \langle 3,\, 4,\, 5 \rangle \] \[ \vec{BC} = \langle 2-4,\, 4-6,\, 5-8 \rangle = \langle -2,\, -2,\, -3 \rangle \]

2. Total distance traveled:

Distance from \( A \) to \( B \):
\[ AB = \sqrt{3^2 + 4^2 + 5^2} = \sqrt{9 + 16 + 25} = \sqrt{50} \approx 7.07 \text{ units} \]
Distance from \( B \) to \( C \):
\[ BC = \sqrt{(-2)^2 + (-2)^2 + (-3)^2} = \sqrt{4 + 4 + 9} = \sqrt{17} \approx 4.12 \text{ units} \]
Distance from \( C \) to \( A \):
\[ \vec{CA} = \langle 1-2,\, 2-4,\, 3-5 \rangle = \langle -1,\, -2,\, -2 \rangle \] \[ CA = \sqrt{(-1)^2 + (-2)^2 + (-2)^2} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3 \text{ units} \]

Total distance covered: \[ AB + BC + CA \approx 7.07 + 4.12 + 3 = \boxed{14.19 \ \text{units}} \]

3. Angle between \( \vec{AB} \) and \( \vec{BC} \):

Let \( \vec{AB} = \langle 3, 4, 5 \rangle \), \( \vec{BC} = \langle -2, -2, -3 \rangle \). Dot product: \[ \vec{AB} \cdot \vec{BC} = (3)(-2) + (4)(-2) + (5)(-3) = -6 – 8 – 15 = -29 \] \(|\vec{AB}| = \sqrt{50} \), \(|\vec{BC}| = \sqrt{17}\) \[ \cos \theta = \frac{\vec{AB} \cdot \vec{BC}}{|\vec{AB}| \ |\vec{BC}|} = \frac{-29}{\sqrt{50} \times \sqrt{17}} \approx \frac{-29}{7.07 \times 4.12} \approx \frac{-29}{29.13} \approx -0.9955 \] \[ \theta = \cos^{-1}(-0.9955) \approx 174.2^\circ \] The angle between \( \vec{AB} \) and \( \vec{BC} \) is approximately \( \boxed{174^\circ} \).

We hope the given case study questions for Vectors Class Class 12 helps you in your learning.

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Topics from which case study questions may be asked

Introduction to Vectors
Types of Vectors
Addition of Vectors
Multiplication of a Vector by a Scalar
Components of a Vector
Vector Joining Two Points
Section Formula (using vectors)
Dot Product (Scalar Product) of Two Vectors
Cross Product (Vector Product) of Two Vectors
Applications of Scalar and Vector Products

Vectors is a fundamental concept in Class 12 Maths, helping students understand its role in advanced mathematical reasoning and problem-solving.

Frequently Asked Questions (FAQs) on Vectors 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 12 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 Vectors case study questions?

A12: We provide case study questions for CBSE Class 12 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.