Vectores. Vectores fijos

Understanding Fixed Vectors

Definition and Characteristics of Fixed Vectors

• A fixed vector is defined as a pair of points in space, with the first point being the origin and the second point being the endpoint. This is denoted as vector AB, represented graphically by an arrow from A to B.

• When both the origin and endpoint coincide, it forms a null fixed vector, such as point C represented simply as C.

• Two fixed vectors are considered consecutive if one’s endpoint coincides with another's origin (e.g., vectors AB and BC). The uniqueness of a fixed vector is determined by its origin and endpoint.

Key Characteristics of Fixed Vectors

1. Modulus

• The modulus of a fixed vector (AB) refers to the length of segment AB. It requires a previously established unit segment for measurement purposes. The modulus of AB equals that of BA, while only null vectors have a modulus of zero.

2. Direction

• Non-null fixed vectors share the same direction if they lie on parallel lines; two lines are parallel if they do not intersect or are coincident within the same plane. For example, vectors AB and CD can be parallel but distinct, indicating they share direction while differing in position.

3. Sense

• Non-null vectors with identical directions on distinct parallel lines have the same sense when their connecting segments do not intersect (e.g., segments AC and BD). Conversely, if segments intersect (like CF and DG), then those vectors have different senses. Additionally, two non-null vectors on the same line will have similar or opposite senses based on their orientation relative to each other or another reference vector.

4. Point of Application