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1.Introduction to Vectors
Class 12 • Mathematics • NCERT
Introduction to Vectors
[ Embed Your Video Lecture Here ]
This lesson introduces vectors, their basic definitions, types, and representation, forming the foundation of vector algebra as prescribed in NCERT Class 12.
Lesson Objectives
- Understand scalar and vector quantities.
- Learn basic terminology related to vectors.
- Represent vectors geometrically.
- Prepare for NCERT board-level questions.
1. Scalars and Vectors
A scalar quantity has only magnitude, whereas a vector quantity has both magnitude and direction.
Examples:
Scalars: mass, time, temperature
Vectors: displacement, velocity, force
Scalars: mass, time, temperature
Vectors: displacement, velocity, force
[ Image Placeholder: Scalar vs Vector Representation ]
2. Vector Definition
A vector is a quantity that has both magnitude and direction and obeys the laws of vector addition.
Vectors are denoted by bold letters or by arrows, e.g. a or →a
[ Image Placeholder: Arrow Representation of a Vector ]
3. Magnitude of a Vector
The magnitude (length) of a vector is denoted by |a| and is always a non-negative real number.
If →a = ai + bj + ck,
|a| = √(a² + b² + c²)
|a| = √(a² + b² + c²)
[ Image Placeholder: Magnitude of a Vector in 2D / 3D ]
4. Types of Vectors
Vectors are classified into different types based on their properties.
• Zero vector
• Unit vector
• Equal vectors
• Collinear vectors
• Unit vector
• Equal vectors
• Collinear vectors
[ Image Placeholder: Different Types of Vectors ]
5. Position Vector
The position vector of a point A with respect to the origin O is the vector →OA.
If A(x, y, z), then →OA = xi + yj + zk
[ Image Placeholder: Position Vector from Origin ]
6. Important NCERT Notes
• Magnitude of vector is always non-negative
• Direction is equally important as magnitude
• Vectors are used extensively in physics and geometry
• Foundation for vector algebra chapter
• Direction is equally important as magnitude
• Vectors are used extensively in physics and geometry
• Foundation for vector algebra chapter
Practice Questions (NCERT)
- Define a vector quantity.
- Give two examples of scalar quantities.
- What is magnitude of a vector?
- Define position vector.
- What is a zero vector?
- What is a unit vector?
- Can magnitude of a vector be negative?
- Write the formula for magnitude of a vector.
- What are collinear vectors?
- Is direction important in vectors?
✅ Show Answer Key
- Quantity with magnitude and direction
- Mass, time
- Length of vector
- Vector from origin to point
- Vector with zero magnitude
- Vector of unit magnitude
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