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RET0 3: MISIÓN VECTORIAL EN ℝ³

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RET0 3: MISIÓN VECTORIAL EN ℝ³

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About this activity

Rumbo a la conquista vectorial

Created by

Shane Walsh
Shane Walsh
Ecuador

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RET0 3: MISIÓN VECTORIAL EN ℝ³
 

RET0 3: MISIÓN VECTORIAL EN ℝ³Online version

Rumbo a la conquista vectorial

by Shane Walsh
1

¿Qué representa un punto en ℝ³?

2

¿Qué indican las coordenadas (x, y, z) de un punto?

3

Si u=(2,3,1) y v=(1,2,4), ¿u+v?

4

Con u=(5,4,6) y v=(2,1,3), ¿u−v?

5

¿Qué indica el producto escalar u·v?

6

Si u=(1,2,3) y v=(2,1,1), ¿u·v?

7

Propiedad de simetría del producto escalar:

8

¿Cómo se define la norma ||u|| de u=(2,3,6)?

9

¿Cómo se calcula la distancia entre p=(x1,y1,z1) y q=(x2,y2,z2)?

10

¿Qué eje corresponde a la coordenada x en un punto (x, y, z)?

11

Si u=(2,0,0) y v=(0,3,0), ¿u·v?

Explicación

¡Correcto! Un punto se representa por (x, y, z).

Exacto, (x, y, z) localizan un punto en ℝ³.

Suma componente a componente debe dar (3,5,5).

Resta componente a componente: (5−2,4−1,6−3)=(3,3,3).

El producto escalar es un número que relaciona direcciones y magnitudes.

1·2 + 2·1 + 3·1 = 2 + 2 + 3 = 7.

El escalar es conmutativo: u·v = v·u.

La norma es la raíz de la suma de cuadrados de sus componentes.

Distancia en ℝ³ usa la raíz de la suma de cuadrados de diferencias.

En (x, y, z), x corresponde al eje X.

Los vectores perpendiculares tienen producto escalar 0.

 
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