Name: using position vectors to locate points
Uploaded: 2025-05-22T09:06:01.000Z
Duration: 1 min 29 s
Channel: JoVE

Un vecteur de position est un vecteur fixe qui localise la position d’un point dans l’espace par rapport à un autre point.
Considérons un œil de vis fixé à un mur et un câble OP attaché à celui-ci. Etablir un système de coordonnées cartésiennes avec l’œil de vis à l’origine et les vecteurs composantes le long des axes pour localiser le point P sur le câble.
Un vecteur de position r dirigé de l’origine au point P peut être exprimé sous forme vectorielle cartésienne.
Pour une représentation générale d’un vecteur cartésien, considérons un support fixé sur un mur et un cordon attaché à celui-ci.
Soient nA et nB les vecteurs position s’étendant de l’origine aux points A et B.
Ainsi, le vecteur de position résultant, n, du point A à B, peut être obtenu en utilisant la règle du triangle et en exprimant nA et nB sous forme vectorielle cartésienne.
i, j et k sont les vecteurs unitaires le long des composantes du vecteur position n formé en soustrayant les coordonnées de A de B.

<ol>
	<li>Russell C. Hibbeler. (2016). Mécanique de l’ingénierie : statique et dynamique. Pearson. (P. N° – 56,57)</li>
</ol>

les vecteurs de position

Un vecteur de position est un concept fondamental en mathématiques qui aide à déterminer la position d'un point par rapport à un autre point dans l'espace. C'est un vecteur qui décrit la direction et la distance entre deux points. Les vecteurs de position sont très utiles dans le domaine des mathématiques et des sciences, car ils aident à représenter les relations spatiales et rendent les calculs plus faciles.

Par exemple, supposons que nous voulons localiser un point P (x, y, z) par rapport à l'origine des coordonnées O. Dans ce cas, nous pouvons définir un vecteur de position r, qui s'étend de l'origine O au point P. Nous pouvons exprimer ce vecteur sous forme cartésienne comme : r = xi + yj + zk, où i, j et k sont les vecteurs unitaires dans les directions x, y et z, respectivement. Le vecteur de position r nous donne la direction et la magnitude du vecteur du point O au point P.

Considérons un vecteur de position dirigé du point A au point B dans l'espace. Ce vecteur peut être désigné par le symbole r. Nous pouvons également nous référer à ce vecteur avec deux indices pour indiquer les points duquel il est dirigé. Ainsi, nous pouvons également désigner r comme rAB. Veuillez noter que si les vecteurs de position s'étendent depuis l'origine des coordonnées, alors ils sont désignés avec seulement un indice, comme rA et rB. Le vecteur de position rAB peut être obtenu à partir de rA et rB en utilisant l'expression rAB = rB - rA = (xB - xA)i + (yB - yA)j + (zB - zA)k. 

Par exemple, pour établir un vecteur de position du point A au point B, on soustrait les coordonnées de la queue A (1 m, 0 m, -3 m) des coordonnées de la tête B (-2 m, 2 m, 3 m), ce qui donne rAB = {-3i + 2j + 6k} m.

Les vecteurs de position

Un vecteur de position est un concept fondamental en mathématiques qui permet de déterminer la position d’un point par rapport à un autre point de l’espace. Il s’agit d’un ...

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Position Vectors

using position vectors to locate points

Position vectors are used to locate points in space and show the direction and distance between two points. In math and science, they help describe spatial relationships and make calculations easier. A position vector can connect one point to another point or show a point’s location relative to the origin of coordinates.

For a point P(x, y, z) relative to the origin O, the position vector r runs from O to P. In Cartesian vector form, it is written as r = x i + y j + z k. Here, i, j, and k are unit vectors in the x, y, and z directions.

The vector r gives both the direction and the magnitude of the path from O to P. When a vector points from point A to point B, it may be written as rAB. Position vectors from the origin use one subscript only, such as rA and rB.

A vector from A to B can be found by subtracting the coordinates of A from the coordinates of B. The relation is rAB = rB - rA = (xB - xA)i + (yB - yA)j + (zB - zA)k. For example, if A is (1 m, 0 m, -3 m) and B is (-2 m, 2 m, 3 m), then rAB = {-3 i + 2 j + 6 k} m.

Using Position Vectors to Locate Points

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key terms and concepts

Learn how position vectors locate points in space, use i, j, k notation, and calculate a vector from one point to another with a clear example.

Using Position Vectors to Locate Points | JoVE K12

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Using Position Vectors to Locate Points

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