Class 10 Maths Chapter 6 Exercise 6.1 Solutions 2026 – Vectors in Plane Notes PDF

Unit 6: Vectors in Plane | Exercise 6.1 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 6.1 solutions for Vectors in Plane have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

A Quantity With Both Size and Direction

Most quantities studied so far — numbers, lengths, areas — are fully described by a single value. A vector is different: it needs both a magnitude (how much) and a direction (which way) to be fully described, like a displacement or a velocity. Exercise 6.1 introduces vectors from scratch, along with the notation and vocabulary used to describe them.

Key Concepts Covered in Exercise 6.1

What a Vector Is

A vector is a quantity having both magnitude and direction, usually represented by a directed line segment (an arrow) from a starting point to an end point, and written as →AB or in bold as a.

Magnitude and Direction

The magnitude of a vector is its length, written |→AB| or |a|, and can be calculated from its components using the Pythagorean theorem: |a| = √(x² + y²) for a vector with components (x, y).

Position Vectors

A position vector describes the location of a point relative to a fixed origin O. The position vector of a point P is simply the vector →OP, and it’s central to describing vectors using coordinates.

Types of Vectors

This exercise introduces several special vectors: the zero vector (magnitude 0, no defined direction), a unit vector (magnitude exactly 1), equal vectors (same magnitude and direction, regardless of starting point), and negative vectors (same magnitude, opposite direction).

Step-by-Step Solved Examples

Q. No. 1: Find the magnitude of the vector a = (3, 4).

|a| = √(x² + y²) = √(3² + 4²)

|a| = √(9 + 16) = √25 = 5

Q. No. 2: Find the position vector of point P(5, −2) relative to the origin O.

The position vector of P is simply →OP = (5, −2)

This is written as →OP = 5i − 2j, using unit vector notation

Q. No. 3: If a = (2, 3) and b = (2, 3), state the relationship between a and b. If c = (−2, −3), state the relationship between a and c.

a and b have identical components, so a = b (they are equal vectors)

c has exactly the opposite components of a, so c = −a (c is the negative vector of a)

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 6.1 in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Exercise

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Quick questions on identifying a unit vector or the zero vector
• Short Questions: Calculating the magnitude of a given vector, like Q. No. 1 above
• Long Questions: Finding position vectors and classifying relationships between multiple given vectors

Where This Matters Beyond This Exercise

Understanding magnitude and direction here is essential for the vector addition and subtraction covered in the next exercise, since combining vectors always depends on their individual components. Vectors themselves are fundamental to physics — describing forces, velocities, and displacements — and to computer graphics, where they define positions and movement in 2D and 3D space.

Common Mistakes Students Make in Exercise 6.1

• Confusing a vector’s magnitude (a single positive number) with the vector itself (which has direction too)
• Writing the position vector of a point incorrectly, such as swapping x and y coordinates
• Assuming two vectors are equal just because they look similar, without checking both magnitude and direction
• Forgetting that the negative of a vector reverses direction but keeps the same magnitude

Why This Exercise Matters for the Board Exam

Exercise 6.1 is largely definitional and notation-based, making it a fast, reliable source of marks in the objective and short-question sections once the vocabulary (magnitude, position vector, unit vector, zero vector) is memorized precisely. A solid grasp here makes the vector arithmetic in later exercises considerably more intuitive.

Quick Links – Chapter 6: Vectors in Plane

Links for sections other than Exercise 6.1 will be activated as they are published on this site.

Download Exercise 6.1 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 6.1 notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. What is the difference between a vector and a scalar?

A scalar is a quantity with only magnitude, such as temperature or mass. A vector has both magnitude and direction, such as displacement or force — this is the key distinction Exercise 6.1 builds on.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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