Displacement Vectors

The displacement vector from one point to another is an arrow with its tail at the first point and its tip at the second.

  • Displacement Vector Notation: \overrightarrow{AB}

Displacement vectors which point in the same direction and have the same magnitude are considered to be the same, even if they do not coincide

The magnitude (or length) of the displacement vector is the distance between the points and is represented by the length of the arrow.

  • Magnitude Notation: \left \| \vec{x} \right \|

Definitions

  • The direction of the displacement vector is the direction of the arrow.

  • \vec{v} vector has both magnitude and direction.

  • v scalar is a quantity with magnitude, but does not have direction.

Addition and Subtraction

The sum of two vectors , \vec{v} + \vec{w} , is the combined displacement of the vectors.

The zero vector, \vec{0}  , is a displacement vector with zero length.

The difference, \vec{v} - \vec{w}  , between two vectors is the displacement vector that, when added to \vec{v}  , gives \vec{w} . This means:

\vec{w} = \vec{v} + \left ( \vec{v} - \vec{w} \right )

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