Class 10 Maths Chapter 6 Exercise 6.2 Solutions 2026 – Vectors in Plane Notes PDF

Unit 6: Vectors in Plane | Exercise 6.2 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 6.2 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.

Combining Vectors Component by Component

Now that Exercise 6.1 has established what a vector is and how to describe it using components, Exercise 6.2 asks how two or more vectors can be combined. The good news is that vector addition, subtraction, and scalar multiplication all work component by component — a familiar pattern from matrix arithmetic in Chapter 3.

Key Concepts Covered in Exercise 6.2

Addition of Vectors

To add two vectors, add their corresponding components: if a = (x₁, y₁) and b = (x₂, y₂), then a + b = (x₁+x₂, y₁+y₂). Geometrically, this matches placing the vectors tail-to-head and drawing the resultant from the first tail to the last head.

Subtraction of Vectors

Subtracting a vector is the same as adding its negative: a − b = a + (−b), which in components becomes (x₁−x₂, y₁−y₂).

Scalar Multiplication

Multiplying a vector by a scalar k stretches or shrinks it (and reverses its direction if k is negative), by multiplying every component by k: ka = (kx, ky).

Combining Operations

Many questions in this exercise combine addition, subtraction, and scalar multiplication in a single expression, such as 2a − 3b, requiring the scalar multiplication to be carried out before combining.

Step-by-Step Solved Examples

Q. No. 1: If a = (3, 2) and b = (−1, 4), find a + b.

a + b = (3+(−1), 2+4)

a + b = (2, 6)

Q. No. 2: If a = (5, 1) and b = (2, 3), find a − b.

a − b = (5−2, 1−3)

a − b = (3, −2)

Q. No. 3: If a = (4, −2), find 3a and −a.

3a = (3×4, 3×(−2)) = (12, −6)

−a = (−4, 2)

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 6.2 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 adding or subtracting two simple vectors
• Short Questions: Scalar multiplication of a given vector, like Q. No. 3 above
• Long Questions: Combined expressions like 2a − 3b, requiring multiple operations in sequence

Where This Matters Beyond This Exercise

Vector addition and subtraction are the foundation for the geometric applications covered in the next exercise, such as finding a resultant force or describing the position of a point using combinations of known vectors. In physics, this exact component-wise approach is how forces, velocities, and accelerations are combined in two-dimensional motion problems.

Common Mistakes Students Make in Exercise 6.2

• Adding magnitudes directly instead of adding corresponding components
• Losing a negative sign when subtracting vectors or multiplying by a negative scalar
• Forgetting that scalar multiplication affects both components, not just one
• Mixing up the order of operations in a combined expression like 2a − 3b

Why This Exercise Matters for the Board Exam

Vector addition, subtraction, and scalar multiplication are quick, formula-based operations that mirror the matrix arithmetic from Chapter 3, making them a dependable and familiar source of marks. Combined expressions are a common long-question style, testing whether multiple operations can be carried out accurately in sequence.

Quick Links – Chapter 6: Vectors in Plane

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 6.2 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. How is vector addition different from adding ordinary numbers?

Vector addition combines corresponding components separately (x with x, y with y), rather than simply adding two single numbers together. The result is itself a vector, with its own magnitude and direction.

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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