Scalar & Vectors
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Scalars, vectors and their paired quantities
A scalar reports a size and nothing else; a vector reports a size plus a direction. The distinction looks small until you meet the paired quantities: distance against displacement, and the route a walker actually takes against the straight line home. This lesson fixes the definitions and the standard pairings.
What you know already
Every measured quantity in this course belongs to one of two families. One family reports only 'how much'; the other also reports 'which way'. This note defines the two families, sorts the familiar pairs — distance and displacement, speed and velocity — and then shows why force itself sits in the second family.
Key points of understanding
- A scalar carries a magnitude only, with no direction attached.
- A vector carries both a magnitude and a direction.
- Distance is the total length of the path travelled, regardless of direction, so it is a scalar.
- Displacement is the straight-line separation of the finishing point from the starting point, including the direction, so it is a vector.
- Mass, energy, volume, density, temperature and power are scalars; weight, force, acceleration and momentum are vectors.
Displacement is a vector quantity while distance is a scalar quantity
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1.Scalars, vectors and their paired quantities
A scalar reports a size and nothing else; a vector reports a size plus a direction. The distinction looks small until you meet the paired quantities: distance against displacement, and the route a walker actually takes against the straight line home. This lesson fixes the definitions and the standard pairings.
Displacement is a vector quantity while distance is a scalar quantity
Key points
- A scalar carries a magnitude only, with no direction attached.
- A vector carries both a magnitude and a direction.
- Distance is the total length of the path travelled, regardless of direction, so it is a scalar.
Guided content from the SME authoring corpus — note rn_4zdmGRWTg5ksK44N, pinned at bfae99778094 · promoted SyllabAI/syllabai-resources b3caaaa90c5e
