Scalars and Vectors
Learning Objectives
- Students will be able to distinguish between scalar and vector quantities
- Students will be able to add vectors graphically and algebraically
- Students will understand vector components and resultants
Core Concepts
- Scalars: magnitude only (speed, mass, time)
- Vectors: magnitude and direction (velocity, acceleration, force)
- Vector addition and subtraction
Formulas
$$R = \sqrt{A^2 + B^2}$$
Pythagorean theorem for vector magnitude
Interesting Fact
The Pythagorean theorem can be used to find the resultant of perpendicular vectors
Key Scientist
Josiah Willard Gibbs
Developed vector analysis and notation in the 19th century
Modern Research
Modern physics treats vectors and tensors as fundamental; Einstein's relativity uses four-vectors to unify space and time into a unified framework.
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