Distributive

Definition

The distributive property is a fundamental algebraic principle that allows for the multiplication of a scalar with a vector sum. Mathematically, it states that $a(b + c) = ab + ac$.

5 Must Know Facts For Your Next Test

1. It applies to both scalar and vector quantities in physics.
2. When distributing a scalar to vector sums, each component of the vector sum is multiplied by the scalar.
3. The distributive property is essential for simplifying vector equations.
4. This property ensures linearity in operations involving vectors and scalars.
5. It is frequently used in mechanics to break down forces into components.

Review Questions

• How does the distributive property apply to the multiplication of a scalar with a vector sum?
• Why is the distributive property important in simplifying vector equations?
• Provide an example where the distributive property helps in breaking down forces into components.

Related terms

Vector:

A quantity that has both magnitude and direction, represented by an arrow.

Scalar:

A quantity that only has magnitude and no direction.

\textit{Linear Combination}: \textit{A combination of vectors formed by adding together multiple vectors scaled by coefficients (scalars).}