Vector addition

Definition

Vector addition is the process of combining two or more vectors to form a resultant vector. The resultant vector represents the cumulative effect of all vectors involved.

5 Must Know Facts For Your Next Test

1. Vectors are added component-wise: add corresponding components to find the resultant vector.
2. The parallelogram law states that if two vectors are represented as adjacent sides of a parallelogram, their sum is given by the diagonal of the parallelogram.
3. The triangle law states that if two vectors are placed head-to-tail, their sum is represented by the vector from the tail of the first to the head of the second.
4. Vector addition is commutative: $\mathbf{A} + \mathbf{B} = \mathbf{B} + \mathbf{A}$.
5. Vector addition is associative: $(\mathbf{A} + \mathbf{B}) + \mathbf{C} = \mathbf{A} + (\mathbf{B} + \mathbf{C})$.

Review Questions

• How do you add vectors using their components?
• What does the parallelogram law state about vector addition?
• Is vector addition commutative and associative? Provide examples.

Related terms

Resultant Vector: The single vector obtained by adding two or more vectors together.

Component Form: A representation of a vector using its horizontal (x) and vertical (y) components.

Magnitude: The length or size of a vector, often calculated using the Pythagorean theorem for its components.