T1-Vectores Asqui

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ESPOCH 
ESCUELA SUPERIOR POLITÉCNICA DE CHIMBORAZO 
 
Fecha: 29’04’2020 
Tema: Vectores 
Materia: Algebra Lineal 
Nombre: Boris Josue Asqui Vaca 
𝐻𝑎𝑙𝑙𝑎𝑟 𝑒𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑜 𝑒𝑠𝑐𝑎𝑙𝑎𝑟 
 
�̅� = (3, −4) |�̅�| = √(3)2 + (−4)2 |�̅�| = 5 
�̅� = (6,8) |�̅�| = √(6)2 + (8)2 |�̅�| = 10 
�̅�. �̅� = |�̅�| ∙ |�̅�| ∙ cos 𝛼 
𝛼 = cos−1
−14
|5| ∙ |10|
 
𝛼 = 106,26 
�̅�. �̅� = (𝑢1 ∙ 𝑣1) + (𝑢2. 𝑣2) 
�̅�. �̅� = (3 ∙ 6) + (−4 ∙ 8) 
�̅�. �̅� = 18 − 32 
�̅�. �̅� = −14 
 
𝐻𝑎𝑙𝑙𝑎𝑟 𝑒𝑙 ángulo 𝑓𝑜𝑟𝑚𝑎𝑑𝑜 𝑝𝑜𝑟 𝑙𝑜𝑠 𝑣𝑒𝑐𝑡𝑜𝑟𝑒𝑠 
 
�̅� = (1,1,3) |�̅�| = √(1)2 + (1)2 + (3)2 |�̅�| = √11 
�̅� = (−1,0,4) |�̅�| = √(−1)2 + (0)2 + (4)2 |�̅�| = √17 
�̅�. �̅� = |�̅�| ∙ |�̅�| ∙ cos 𝛼 
𝛼 = cos−1
11
|√11| ∙ |√17|
 
𝛼 = 36.44 
�̅�. �̅� = (𝑢1 ∙ 𝑣1) + (𝑢2. 𝑣2) 
�̅�. �̅� = (1 ∙ −1) + (0 ∙ 1) + (3 ∙ 4) 
�̅�. �̅� = −1 + 12 
�̅�. �̅� = 11