Vectors Examples in Physics
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Vectors.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.
Concept Recap
Mathematical quantities that have both a magnitude (size) and a direction, represented as arrows in diagrams.
An arrow pointing somewhere with a certain length—the length is 'how much,' the direction is 'which way.'
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: Vectors capture directional quantities; scalars (like mass) don't have direction.
Common stuck point: Adding vectors isn't like adding numbers—you must account for direction.
Worked Examples
Example 1
easySolution
- 1 Use the Pythagorean theorem for the magnitude of the vector.
- 2 Magnitude: |\vec{v}| = \sqrt{v_x^2 + v_y^2} = \sqrt{9 + 16} = \sqrt{25} = 5
- 3 Direction: \theta = \tan^{-1}\left(\frac{v_y}{v_x}\right) = \tan^{-1}\left(\frac{4}{3}\right) \approx 53.1°
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.