Vector Addition is a fundamental and high-scoring topic in your Karnataka Diploma Mathematics examination. Questions on adding two or more vectors are guaranteed in the paper, making it an essential concept for securing your passing marks. The Ravi R Nandi YouTube channel is your go-to resource for mastering this topic with simple, exam-oriented methods.
📘 The Formula: Algebraic Vector Addition
The simplest and most direct way to add vectors for the exam is through the algebraic (or component) method, especially for problems involving the $\hat{i}$, $\hat{j}$, and $\hat{k}$ unit vectors in three dimensions.
The Component Method
If you have two vectors, $\vec{A}$ and $\vec{B}$, defined by their components:
- $\vec{A} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}$
- $\vec{B} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}$
The resultant vector 1$\vec{R}$ is the sum of the two vectors, found by simply adding the corresponding components:2
$$\vec{R} = \vec{A} + \vec{B} = (a_1 + b_1)\hat{i} + (a_2 + b_2)\hat{j} + (a_3 + b_3)\hat{k}$$
Solved Example (Exam Style)
Question: If $\vec{A} = 3\hat{i} – 2\hat{j} + 5\hat{k}$ and $\vec{B} = \hat{i} + 4\hat{j} – \hat{k}$, find the sum of the two vectors, $\vec{A} + \vec{B}$.
Solution Steps:
- Group $\hat{i}$ components: $3\hat{i} + 1\hat{i} = (3 + 1)\hat{i} = 4\hat{i}$
- Group $\hat{j}$ components: $-2\hat{j} + 4\hat{j} = (-2 + 4)\hat{j} = 2\hat{j}$
- Group $\hat{k}$ components: $5\hat{k} – 1\hat{k} = (5 – 1)\hat{k} = 4\hat{k}$
Final Answer:
$$\vec{A} + \vec{B} = 4\hat{i} + 2\hat{j} + 4\hat{k}$$
This type of problem is a classic 2 or 3-mark question in the Karnataka Diploma Maths paper.
📺 Learning with Ravi R Nandi
For a deep and simplified understanding, the Ravi R Nandi YouTube channel is highly recommended. Ravi R Nandi Sir focuses specifically on content relevant to the Karnataka Diploma syllabus (including C20 and C25 curriculum), ensuring you only spend time on what matters most for the exam.3
- Look for the Video: Search for the video titled “01 | Sum & Dot Product of Two Vectors | Easy for Karnataka Diploma Students | Ravi R Nandi” or similar titles in his playlists. This lesson explicitly covers the simple, algebraic method for finding the sum of two vectors.
- Passing Package Focus: His “Passing Package” videos often feature a selection of mandatory, repeating questions. Vector Addition is consistently included in these lists, giving you focused practice.
- Step-by-Step Clarity: Ravi R Nandi’s style involves clear, step-by-step guidance, which is essential for ensuring you write the solution correctly in the exam to fetch full marks.4
✅ Final Advice for Success
To ensure you not only pass but also score well, you must practice two things related to vector addition:
- Vector Subtraction: Know that $\vec{A} – \vec{B}$ is just the addition of $\vec{A}$ and $(-\vec{B})$. The process is the same: subtract the corresponding components.
- Magnitude of the Resultant: After finding the sum vector $\vec{R}$, you may be asked to find its magnitude $|\vec{R}|$. You must know the formula: $|\vec{R}| = \sqrt{R_x^2 + R_y^2 + R_z^2}$.
🔔 Your Path to Better Results: Subscribe Now!
The Ravi R Nandi YouTube Channel provides dedicated support, timely exam updates, and curated “Passing Packages” for Karnataka Diploma students.5 By subscribing and turning on notifications, you ensure you never miss out on the crucial tips, important questions, and simplified lessons that can make the difference between passing and excelling in your final exams.
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