Exercise 6.1 Class 10 Math Solutions – Vectors in Plane & Position Vectors, Punjab Board

Solved Exercise 6.1 for Class 10 Mathematics, Punjab Board. Comprehensive step-by-step notes covering scalars vs vectors, directed line segments, position vectors in the Cartesian plane, magnitude calculations, scalar multiplication, and unit vectors.

This page provides complete solved solutions for Exercise 6.1 from Unit 6: Vectors in Plane, Class 10 Mathematics, Punjab Board (PCTB). It introduces vectors and scalars, geometric representation via directed line segments, Cartesian coordinate components, position vectors, magnitude calculation using √(x² + y²), scalar multiplication, and determining unit vectors. All problems are fully solved with step-by-step working for Matric Part 2 students.
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Exercise Overview

Exercise 6.1 marks the start of Unit 6: Vectors in Plane in the Class 10 Punjab Board Mathematics curriculum. This foundational exercise introduces students to two-dimensional vector algebra in the Cartesian coordinate plane, establishing the essential distinction between scalar quantities (possessing only magnitude) and vector quantities (possessing both magnitude and direction).

The exercise systematically develops analytical geometry skills: representing vectors as directed line segments from initial to terminal points, defining position vectors originating at the origin O(0, 0), and expressing vectors in component form as ordered pairs (x, y) or unit-vector notation x i + y j. Students learn and apply standard formulas to compute vector magnitude |u| = √(x² + y²), perform scalar multiplication ku = (kx, ky), and construct unit vectors û = u / |u| in the direction of given vectors.

In Punjab Board examinations across Lahore, Rawalpindi, Faisalabad, Gujranwala, Multan, and other BISE boards, Exercise 6.1 provides core material for objective MCQs and 4-mark short questions in Section B. Understanding these introductory definitions and component calculations is critical for tackling subsequent dot products and vector applications.

FAQs

Are these Exercise 6.1 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 6.1 plane vector concepts for the 2026-2027 session.
What is the difference between a scalar and a vector in Mathematics?
A scalar has only magnitude (e.g., mass, distance, time), whereas a vector has both magnitude and a specific direction (e.g., displacement, velocity, force).
How is a vector represented in a rectangular coordinate plane?
A vector is represented geometrically as a directed line segment with an initial point and a terminal arrow, or algebraically as an ordered pair (x, y) or in component form xi + yj.
What is a position vector?
A position vector is a vector whose initial point is fixed at the origin O(0, 0) of the Cartesian plane and whose terminal point is at any point P(x, y), denoted as OP or r.
How do you calculate the magnitude (length) of a vector in a plane?
For a vector u = (x, y) or u = xi + yj, the magnitude is calculated using the Pythagorean formula: |u| = √(x² + y²).
What is a unit vector and how is it determined?
A unit vector has a magnitude of exactly 1. It is found by dividing a non-zero vector u by its magnitude: û = u / |u| = (xi + yj) / √(x² + y²).
What happens when a vector is multiplied by a scalar?
Multiplying vector u = (x, y) by scalar k gives ku = (kx, ky). If k > 0, direction is unchanged; if k < 0, direction reverses; and magnitude becomes |k||u|.
Can students read these Exercise 6.1 solutions online?
Yes, the complete solved PDF notes for Exercise 6.1 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 6.1 solutions free for students?
Yes, all Exercise 6.1 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.