Exercise 6.2 Class 10 Math Solutions – Vector Addition, Subtraction & Coplanar Vectors, Punjab Board

Solved Exercise 6.2 for Class 10 Mathematics, Punjab Board. Comprehensive step-by-step notes covering Triangle Law of Addition, Parallelogram Law of Addition, difference of vectors, and expressing vectors in terms of non-parallel coplanar vectors.

This page provides complete solved solutions for Exercise 6.2 from Unit 6: Vectors in Plane, Class 10 Mathematics, Punjab Board (PCTB). It covers vector addition using the Triangle Law and Parallelogram Law, vector subtraction, algebraic component operations, and expressing any vector as a linear combination of two non-zero, non-parallel coplanar vectors. All problems are solved with step-by-step working for Matric Part 2 students.
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Exercise Overview

Exercise 6.2 in Unit 6: Vectors in Plane of Class 10 Punjab Board Mathematics expands upon foundational vector concepts by examining vector operations and algebraic geometry laws. This exercise focuses on both geometric and algebraic methods for combining and resolving two-dimensional vectors in a plane.

Students learn the foundational geometric principles of vector addition: the Triangle Law (head-to-tail method) and the Parallelogram Law (co-initial vectors). The exercise extends these laws to define vector subtraction as the addition of an opposite vector, u - v = u + (-v). In addition, students master the algebraic resolution of vectors into Cartesian components and learn to express any arbitrary coplanar vector r as a unique linear combination r = xa + yb of two non-collinear basis vectors a and b by setting up and solving simultaneous linear equations.

In Punjab Board examinations (including BISE Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, Sargodha, Bahawalpur, and DG Khan), questions from Exercise 6.2 frequently appear in Section B as 4-mark short questions and in Section C as multi-part proofs and linear combination problems. These detailed, step-by-step solutions provide the rigorous algebraic working needed for full marks.

FAQs

Are these Exercise 6.2 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, covering all Unit 6 Exercise 6.2 vector addition, subtraction, and coplanar vector topics for the 2026-2027 session.
What is the Triangle Law of Vector Addition?
The Triangle Law states that if two vectors are represented in magnitude and direction by two sides of a triangle taken in order (head to tail), their resultant is represented by the third side taken in reverse order.
What is the Parallelogram Law of Vector Addition?
The Parallelogram Law states that if two vectors acting at a point are represented by adjacent sides of a parallelogram, their resultant vector is represented by the diagonal passing through their common initial point.
How do you find the difference of two vectors (u - v)?
The difference u - v is defined as the sum of vector u and the negative vector (-v): u - v = u + (-v). Geometrically, it joins the terminal point of v to the terminal point of u.
How is vector addition performed algebraically using components?
To add u = (x₁, y₁) and v = (x₂, y₂), add corresponding horizontal and vertical components: u + v = (x₁ + x₂, y₁ + y₂) or (x₁ + x₂)i + (y₁ + y₂)j.
How can any coplanar vector be expressed in terms of two non-zero, non-parallel vectors?
Any coplanar vector r can be uniquely written as a linear combination r = xa + yb, where a and b are non-zero, non-parallel coplanar vectors, and x, y are unique scalar multipliers.
Are all questions in Exercise 6.2 solved with step-by-step geometric and algebraic steps?
Yes, each problem is solved with complete algebraic component working, vector laws, scalar equations, and geometric justifications.
Can students read these Exercise 6.2 solutions online?
Yes, the complete solved PDF notes for Exercise 6.2 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 6.2 solutions free for students?
Yes, all Exercise 6.2 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.