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Vector addition is a fundamental concept in physics, engineering, and mathematics, involving the combination of vectors to form a resultant. This process can be performed algebraically by adding corresponding components or geometrically using the Triangle or Parallelogram Laws. Understanding zero vectors, additive inverses, and vector subtraction is essential for applications in real-world scenarios, such as combining forces or calculating displacements.

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## Definition of Vector Addition

### Algebraic Method

Vector addition involves adding the corresponding components of each vector

### Geometric Method

Triangle Law

The Triangle Law involves connecting the tail of one vector to the tip of another to find the resultant vector

Parallelogram Law

The Parallelogram Law involves constructing a parallelogram with the vectors as sides to find the resultant vector

### Properties of Vector Addition

Vector addition is commutative and associative, and the zero vector and additive inverse play important roles in the operation

## Applications of Vector Addition

### Forces

Vector addition is used in physics to combine forces acting on an object

### Displacements

Vector addition is used in physics to find the total displacement of an object

### Other Vector Quantities

Vector addition is used in various fields, such as engineering and mathematics, to combine other vector quantities

## Definition of Vector Subtraction

### Algebraic Method

Vector subtraction involves adding the additive inverse of a vector to another vector

### Geometric Method

Vector subtraction can be visualized using the Parallelogram Law, where the inverse vector is drawn in the opposite direction

### Applications of Vector Subtraction

Vector subtraction is used in physics to find the difference between two vector quantities, such as forces or displacements

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