Difference of two vectors

Definition

The difference of two vectors is found by subtracting the corresponding components of the vectors. The resulting vector points from the tip of the second vector to the tip of the first vector.

5 Must Know Facts For Your Next Test

1. To subtract vectors, subtract their corresponding components: $$\mathbf{C} = \mathbf{A} - \mathbf{B}$$ where $$\mathbf{C}$$ is the resultant vector.
2. Graphically, vector subtraction involves reversing the direction of the second vector and then performing vector addition.
3. The magnitude of the difference between two vectors can be found using the Pythagorean theorem for orthogonal components.
4. Vector subtraction is not commutative; $$\mathbf{A} - \mathbf{B} \neq \mathbf{B} - \mathbf{A}$$.
5. In physics, this operation is often used to determine relative velocity or displacement.

Review Questions

• How do you find the difference between two vectors graphically?
• What is the formula for subtracting two vectors component-wise?
• Why is vector subtraction not commutative?

Related terms

Vector Addition: Combining two or more vectors to produce their sum by adding corresponding components.

Magnitude: The length or size of a vector, calculated as $$\sqrt{x^2 + y^2 + z^2}$$ for a three-dimensional vector.

Unit Vector: A vector with a magnitude of one that indicates direction only.