Class 10 Math Unit 6 Exercise 6.1 Solved – Vectors in Plane (PECTAA 2026)

Class 10 Math Unit 6 Exercise 6.1 – Vectors in Plane: Complete Guide

Unit 6 of Class 10 Mathematics introduces students to vectors in the plane, one of the most visual and application-rich topics in the PECTAA 2026 syllabus. Exercise 6.1 is the entry point into this chapter, and it lays the groundwork that every later exercise in Unit 6 — including Exercise 6.2, Exercise 6.3, and the Unit 6 Review Exercise — builds on. This page walks through every question of Exercise 6.1 step by step, prepared according to the unified Punjab textbook used across all 10 BISE Punjab boards.

What You Will Learn

By working through Exercise 6.1, students learn how to identify the four quadrants of the Cartesian plane, plot points and vectors accurately, write a vector in the standard form \(x\hat{i} + y\hat{j}\), calculate the magnitude of a vector using the distance-style formula, convert any vector into a unit vector, and test two vectors for parallelism using the scalar multiple condition. These are not isolated skills — they are the building blocks used throughout the rest of Unit 6 and reappear in Unit 7 (Trigonometry) when vectors are combined with angles and direction.

Topics Covered in This Exercise

• Quadrants and coordinate points – naming the quadrant in which a given point lies
• Plotting points and vectors – representing coordinates visually on the Cartesian plane
• Tail and tip of a vector – identifying the starting and ending points of a vector from a diagram
• Vector notation – writing a vector \(\overrightarrow{AB}\) as \(\overrightarrow{OB} - \overrightarrow{OA}\) in the form \(x\hat{i} + y\hat{j}\)
• Magnitude of a vector – using \(|\bar{a}| = \sqrt{x^2 + y^2}\)
• Unit vectors – finding \(\hat{a} = \bar{a} / |\bar{a}|\)
• Parallel vectors – checking whether \(\bar{b} = \lambda \bar{a}\) for some scalar \(\lambda\)

Why Exercise 6.1 Is Important

Exercise 6.1 is the foundation exercise of Unit 6. Punjab Board exam papers frequently draw at least one short question directly from this exercise, particularly on magnitude, unit vectors, and parallel vectors, because these three concepts are easy to test in a single line and easy for examiners to vary slightly from year to year. Students who skip Exercise 6.1 and jump straight into Exercise 6.2 or Exercise 6.3 often struggle, because those exercises assume fluency with the notation and formulas introduced here.

Punjab Board Preparation

For students preparing for board exams under any of the 10 BISE Punjab boards, this exercise should be treated as compulsory practice rather than optional revision. The magnitude formula, the unit vector formula, and the parallel vector condition \((\bar{b} = \lambda \bar{a})\) are the three most commonly repeated question types from Unit 6 in past board papers. Practising every part of Q5, Q6, and Q9 by hand — not just reading the worked solution — is the single most effective way to prepare for this portion of the paper.

PECTAA 2026 Syllabus Alignment

These solved notes are aligned with the Punjab Education & Curriculum Textbook Authority (PECTAA) 2026 syllabus, which follows the National Curriculum 2023 framework for Class 10 Mathematics. The question numbering, formulas, and terminology used on this page match the current Punjab textbook exactly, so students can use it alongside their school textbook without any mismatch in question order or notation.

Exam Tips for Vectors in Plane

• Always simplify the magnitude under the square root fully before writing the final answer (e.g. \(\sqrt{4} + \sqrt{9}\) should combine into a single simplified surd where possible).
• When writing a unit vector, keep the denominator as the exact magnitude — do not round it to a decimal, since board examiners award marks for exact surd or fraction form.
• For parallel vector questions, always state the value of the scalar \(\lambda\) explicitly; simply saying "they are parallel" without showing \(\bar{b} = \lambda \bar{a}\) loses marks.
• Double-check the direction of subtraction in \(\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA}\) — a common source of sign errors.

Common Mistakes Students Make

• Confusing \(\overrightarrow{AB}\) with \(\overrightarrow{BA}\) and getting the sign of the vector reversed.
• Forgetting to square negative components correctly when computing magnitude (e.g. treating \((-3)^2\) as \(-9\) instead of \(9\)).
• Leaving the unit vector un-simplified, or forgetting to rationalise a denominator when required.
• Assuming two vectors are parallel just because their magnitudes look similar, instead of checking \(\bar{b} = \lambda \bar{a}\).

Use the table of contents below to jump directly to any question, or scroll through the full solved exercise in order.