Vector Addition Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Vector Addition.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Vector addition combines vectors component-wise or head-to-tail to produce a resultant vector.
Walk one arrow, then another; the single shortcut arrow is their sum.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Add corresponding components to combine directions and magnitudes.
Common stuck point: You cannot add vector magnitudes alone — direction matters; add each component separately instead.
Sense of Study hint: Draw arrows or write components before adding.
Worked Examples
Example 1
easySolution
- 1 Step 1: Add corresponding components: (2 + (-1), 1 + 3).
- 2 Step 2: = \langle 1, 4 \rangle.
- 3 Check: Geometrically, this is the diagonal of a parallelogram formed by the two vectors ✓
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.