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

Un vettore di posizione è un vettore fisso che individua la posizione di un punto nello spazio rispetto a un altro punto.
Considera un occhiello a vite fissato a una parete e un cavo OP collegato ad esso. Stabilire un sistema di coordinate cartesiane con l'occhiello della vite all'origine e i vettori dei componenti lungo gli assi per individuare il punto P sul cavo.
Un vettore di posizione r diretto dall'origine al punto P può essere espresso in forma vettoriale cartesiana.
Per una rappresentazione generale di un vettore cartesiano, si consideri una staffa fissata su una parete e un cavo attaccato ad essa.
Siano nA e nB i vettori di posizione che si estendono dall'origine ai punti A e B.
Quindi il vettore di posizione risultante n dal punto A al punto B, può essere ottenuto utilizzando la regola del triangolo ed esprimendo nA e nB nella forma vettoriale cartesiana.
i, j e k sono i vettori unitari lungo le componenti del vettore di posizione n formato sottraendo le coordinate di A da B.

<ol>
	<li>Russell C. Hibbeler. (2016). Ingegneria meccanica: statica e dinamica. Pearson. (Pag. No – 56,57)</li>
</ol>

vettori di posizione

Un vettore di posizione è un concetto fondamentale in matematica che aiuta a determinare la posizione nello spazio di un punto rispetto a un altro. È un vettore che descrive la direzione e la distanza tra due punti. I vettori di posizione sono molto utili nel campo della matematica e della scienza, poiché aiutano a rappresentare le relazioni spaziali e rendono più semplici i calcoli.

Ad esempio, vogliamo individuare un punto P(x, y, z) rispetto all'origine delle coordinate O. In tale caso, possiamo definire un vettore di posizione r, che si estende dall'origine O al punto P. Possiamo esprimere questo vettore in forma vettoriale cartesiana come: r = xi + yj + zk, dove i, j e k sono i vettori unitari nelle direzioni x, y e z, rispettivamente. Il vettore di posizione r ci fornisce la direzione e la grandezza del vettore dal punto O al punto P.

Consideriamo un vettore di posizione diretto dal punto A al punto B nello spazio. Questo vettore può essere indicato con il simbolo r. Possiamo anche riferirci a questo vettore con due pedici per indicare i punti da cui e verso cui è diretto. Pertanto, possiamo designare r come rAB. Si noti che se i vettori di posizione si estendono dall'origine delle coordinate, allora vengono indicati con un solo pedice, come rA e rB. Il vettore di posizione rAB può essere ottenuto da rA e rB usando l'espressione rAB = rB - rA = (xB - xA)i + (yB - yA)j + (zB - zA)k.

Ad esempio, per stabilire un vettore di posizione dal punto A al punto B, le coordinate del punto di partenza A(1 m, 0 m, -3 m) vengono sottratte alle coordinate della destinazione B(-2 m, 2 m, 3 m), ottenendo così rAB = { -3i + 2j + 6k} m.

Vettori di posizione

Un vettore di posizione è un concetto fondamentale in matematica che aiuta a determinare la posizione di un punto rispetto a un altro punto nello spazio. Si tratta di un ...

Education

Didattica

JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Force Vectors

Vettori di forza

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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cross product

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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

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Using Position Vectors to Locate Points

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