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Scalar quantity definition
Quantity with magnitude only
Vector quantity definition
Quantity with magnitude and direction
Examples of scalars
Speed, distance, mass, time, energy, temperature
Examples of vectors
Velocity, displacement, acceleration, force, momentum
Speed vs velocity
Speed is scalar; velocity is vector
Distance vs displacement
Distance is scalar; displacement is vector
Adding scalars
Add normally
Adding vectors
Must consider direction
Vector representation
Arrow showing magnitude and direction
Resultant vector
Single vector with same effect as all vectors combined
Opposite direction vectors
Subtract magnitudes
Same direction vectors
Add magnitudes
Right‑angle vectors
Use Pythagoras to find resultant
Vector diagram
Arrows drawn tip‑to‑tail
Scalar cannot cancel
Only vectors can cancel due to direction
Key idea
Scalars have size only; vectors have size and direction