Vector Addition
Add component-wise; geometrically tip-to-tail.
Key idea
Add component-wise; geometrically tip-to-tail.
In depth
Add vectors component by component, or geometrically by placing them tip to tail (parallelogram rule). Addition is commutative and associative, and the zero vector is the identity.
Worked example
(2, 1) + (−1, 4) = (1, 5).
Formula
Real-world uses
- Combining the walking and boat velocities to find the true path of a ferry across a river
Common mistake
Adding vectors of different dimensions; they must have the same number of components.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Vector Addition?
Add component-wise; geometrically tip-to-tail. It is a topic at the intermediate level in Linear Algebra.
What is the formula for Vector Addition?
The key formula is u + v = (u₁+v₁, u₂+v₂).
Where is Vector Addition used in real life?
Real-world examples: Combining the walking and boat velocities to find the true path of a ferry across a river.
What should I learn before Vector Addition?
Make sure you are comfortable with Vector Notation and Components, the previous topic in Linear Algebra.
What is a common mistake with Vector Addition?
Adding vectors of different dimensions; they must have the same number of components.
How can I practise Vector Addition?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Vector Addition?
Move on to Scalar Multiplication next.
Related intermediate topics in Linear Algebra
- Scalars and Vectors – A scalar is a number; a vector has magnitude and direction.
- Vector Notation and Components – Write vectors as ordered lists of coordinates.
- Scalar Multiplication – Scale a vector’s length.
- Vector Magnitude – Length of a vector.
- Unit Vectors – Vectors of length 1, found by normalising.
- Matrices: Definition – A rectangular array of numbers with m rows and n columns.