A position vector is a fundamental concept in mathematics that helps determine the position of one point with respect to another point in space. It is a vector that describes the direction and distance between two points. Position vectors are highly useful in the field of math and science, as they help represent spatial relationships and make calculations easier.

For instance, we want to locate a point P(x, y, z) relative to the origin of coordinates O. In that case, we can define a position vector r, which extends from the origin O to point P. We can express this vector in Cartesian vector form as: r = xi + yj + zk, where i, j, and k are the unit vectors in the x, y, and z directions, respectively. The position vector r gives us the direction and magnitude of the vector from point O to point P.

Consider a position vector directed from point A to point B in space. This vector can be denoted by the symbol r. We can also refer to this vector with two subscripts to indicate the points from and to which it is directed. Thus, we can also designate r as rAB. Please note that if the position vectors extend from the origin of coordinates, then they are referred to only with one subscript, as rA and rB. The position vector rAB can be obtained from rA and rB using the expression rAB = rB - rA= (xB - xA)i + (yB - yA)j + (zB - zA)k.

For example, to establish a position vector from point A to B, the coordinates of the tail A(1 m, m0, -3 m) are subtracted from the coordinates of the head B(-2 m, 2 m, 3 m), which yields rAB={ -3i + 2j + 6k} m.

Tags
Position VectorMathematicsSpatial RelationshipsCartesian Vector FormUnit VectorsCoordinatesMagnitudeDirectionVector NotationRABVector CalculationPoint APoint B

Aus Kapitel 2:

article

Now Playing

2.13 : Position Vectors

Force Vectors

632 Ansichten

article

2.1 : Skalar und Vektoren

Force Vectors

1.1K Ansichten

article

2.2 : Vektor-Operationen

Force Vectors

1.0K Ansichten

article

2.3 : Einführung in die Kraft

Force Vectors

381 Ansichten

article

2.4 : Klassifizierung der Kräfte

Force Vectors

976 Ansichten

article

2.5 : Vektoraddition von Kräften

Force Vectors

491 Ansichten

article

2.6 : Zweidimensionales Kraftsystem

Force Vectors

769 Ansichten

article

2.7 : Zweidimensionales Kraftsystem: Problemlösung

Force Vectors

468 Ansichten

article

2.8 : Skalare Notation

Force Vectors

583 Ansichten

article

2.9 : Kartesische Vektornotation

Force Vectors

585 Ansichten

article

2.10 : Richtungskosinus eines Vektors

Force Vectors

322 Ansichten

article

2.11 : Dreidimensionales Kraftsystem

Force Vectors

1.8K Ansichten

article

2.12 : Dreidimensionales Kraftsystem: Problemlösung

Force Vectors

519 Ansichten

article

2.14 : Kraftvektor entlang einer Linie

Force Vectors

392 Ansichten

article

2.15 : Skalarprodukt

Force Vectors

230 Ansichten

See More

JoVE Logo

Datenschutz

Nutzungsbedingungen

Richtlinien

Forschung

Lehre

ÜBER JoVE

Copyright © 2025 MyJoVE Corporation. Alle Rechte vorbehalten