Higher MathVector QuantityNCTB উচ্চতর গণিত অধ্যায় ১২ (সমতলীয় ভেক্টর)
Vector & Magnitude
Bengali: ভেক্টর ও পরম মান•Pronunciation: ভেক্টর অ্যান্ড ম্যাগনিচ্যুড•Symbol: \vec{v} = x\hat{i} + y\hat{j}
Standard Definition:
A geometric entity possessing both magnitude and spatial direction, adhering to the vector parallelogram laws of addition.
📐 Mathematical Equation, Units & Dimensions
Defining Mathematical Equation
Standard SI Unit
Depends on physical nature(রাশির প্রকৃতির ওপর নির্ভরশীল)
Dimensional Analysis
CGS Unit
None
📖 Physical Concept & Comprehensive Explanation
Vectors combine magnitude and direction. In 2D Cartesian coordinates, v = x*i + y*j with magnitude |v| = sqrt(x^2 + y^2). Vectors obey triangle and parallelogram laws of addition rather than elementary scalar algebra.
🎯 High-Yield Revision Points
- ✓Requires both magnitude and direction.
- ✓Magnitude: |v| = sqrt(x^2 + y^2).
- ✓Unit vector: vector divided by its scalar magnitude.
Use Online Solver for Vector & Magnitude
Compute step-by-step solutions, verify formulas, and plot interactive diagrams on biggan.me.
❓ Frequently Asked Exam Questions (FAQ)
Common questions in board and competitive entrance examinations
Q1: What are unit and null vectors?
A unit vector has a magnitude of 1. A null (zero) vector has zero magnitude and an indeterminate direction.