Vectors
A vector is a quantity that has both magnitude and direction. Vectors are widely used in mathematics, physics, and engineering to represent physical quantities like force, velocity, and displacement.
Types of Vectors
- Position Vector: Represents a point in space relative to the origin
- Zero Vector: Vector with zero magnitude
- Unit Vector: Vector with magnitude equal to 1
- Equal Vectors: Vectors with same magnitude and direction
- Parallel and Anti-parallel Vectors: Same or opposite directions
Vector Operations
- Addition: Combining two or more vectors
- Subtraction: Finding the difference between vectors
- Scalar Multiplication: Changing magnitude by a scalar
- Dot Product (Scalar Product): Measures projection
- Cross Product (Vector Product): Gives a vector perpendicular to the plane
Applications of Vectors
- Physics: force, velocity, and acceleration analysis
- Engineering: stress, torque, and motion studies
- Computer graphics: 3D modeling and animation
- Navigation: displacement and direction calculations
Conclusion
Vectors are fundamental for representing magnitude and direction in mathematics and physics. Understanding vector types and operations is essential for engineering, computer graphics, and real-world problem solving.