Name: adding and multiplying vectors
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 20 s
Channel: JoVE

Considere dos vectores de fuerza en un sistema de coordenadas bidimensional.
Estos vectores se pueden sumar usando la ley del paralelogramo, donde las colas de los vectores concurrentes se unen y las líneas paralelas a cada vector se dibujan para formar un paralelogramo.
El vector resultante se puede obtener dibujando una diagonal desde las colas hasta el punto de intersección de las líneas.
De manera similar, los vectores se pueden sumar usando la regla del triángulo, donde dos vectores están dispuestos como dos lados del triángulo unidos cara a cola, y el tercer lado del triángulo representa la magnitud y la dirección del vector resultante.
La resta de vectores es similar a sumar el inverso de un vector a otro. Como resultado, la diferencia entre dos vectores se obtiene utilizando las mismas reglas de suma de vectores.
Cuando un vector se multiplica por un escalar, la magnitud del vector varía por la cantidad del escalar.
Si el escalar es positivo, entonces la dirección del vector sigue siendo la misma, y si es negativo, la dirección se invierte.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 18 -19</li>
</ol>

operaciones de vectores

Los vectores son cantidades físicas que tienen tanto magnitud como dirección. Las operaciones de vectores incluyen la suma, la resta y la multiplicación escalar. Un vector multiplicado por un valor escalar se llama multiplicación escalar. El resultado obtenido es un nuevo vector con una magnitud diferente. Si el escalar es positivo, la dirección del vector permanece igual, pero si es negativo, la dirección del vector se invierte. Por ejemplo, el producto de la masa y la velocidad da como resultado el momento. Aquí, la cantidad escalar masa se multiplica por la cantidad vectorial velocidad, lo que resulta en la cantidad vectorial momento. La dirección del vector resultado del momento es la misma dirección que el vector velocidad. Los dos vectores se pueden sumar geométricamente utilizando la ley del paralelogramo de la suma de vectores. Al sumarlos utilizando esta ley, los dos vectores se representan como lados adyacentes de un paralelogramo. Las colas de ambos vectores se colocan en el origen y las líneas paralelas a cada vector se dibujan para formar un paralelogramo. Luego, se dibuja la diagonal del paralelogramo desde el origen hasta la esquina opuesta del paralelogramo para representar el vector resultante. La magnitud y dirección del vector resultante se pueden determinar midiendo la longitud y los ángulos de la diagonal del paralelogramo. La ley del paralelogramo se puede simplificar en un escenario especial donde los dos vectores son colineales, es decir, tienen la misma línea de acción. En este caso, el vector resultante se puede obtener mediante una suma algebraica o escalar de los dos vectores. Otro método para sumar gráficamente dos vectores es la ley del triángulo de la suma de vectores. La regla del triángulo de la suma de vectores establece que si se colocan dos vectores juntos cabeza con cola como dos lados de un triángulo, el tercer lado del triángulo representa la magnitud y dirección del vector resultante. La suma de vectores utilizando esta ley implica colocar el primer vector en el origen y colocar el segundo vector cabeza con cola junto al primer vector. El tercer lado del triángulo desde el origen hasta el final del segundo vector representa el vector resultante. El proceso de resta de vectores implica sumar el reverso (negativo) de un vector a otro vector. Esto significa que las reglas de la suma de vectores se pueden aplicar para obtener la diferencia entre los dos vectores.

Operaciones de vectores

Los vectores son cantidades físicas que tienen magnitud y dirección. Las operaciones vectoriales incluyen la suma, la resta y la multiplicación escalar.
Un...

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Force Vectors

Vectores de fuerza

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Vector Operations

adding and multiplying vectors

Vectors are quantities with both magnitude and direction, and their operations include addition, subtraction, and scalar multiplication. Scalar multiplication means a vector is multiplied by a scalar value, which creates a new vector with a different magnitude. If the scalar is positive, the direction stays the same. If the scalar is negative, the direction reverses.

A common example is momentum, which comes from multiplying mass by velocity. In this case, mass is the scalar quantity and velocity is the vector quantity. The result is momentum, and its direction matches the direction of the velocity vector.

Two vectors can be added geometrically with the parallelogram law. In this method, the two vectors are drawn as adjacent sides of a parallelogram with both tails at the origin. Lines are then drawn parallel to each vector to complete the shape.

The diagonal of the parallelogram, drawn from the origin to the opposite corner, shows the resultant vector. Its magnitude and direction can be found by measuring the diagonal's length and angles. When the two vectors are collinear, meaning they share the same line of action, the resultant can be found by algebraic or scalar addition.

Another way to add vectors is the triangle law of vector addition. Here, the vectors are arranged head to tail as two sides of a triangle. The third side of the triangle, from the origin to the end of the second vector, represents the resultant vector.

Vector subtraction uses the reverse, or negative, of one vector added to another vector. This lets the rules of vector addition be used to find the difference between two vectors.

Adding and Multiplying Vectors

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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

Adding and Multiplying Vectors

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