Math Problem Statement

Dados los vectores 𝑢⃗ = 5𝑖̂ − 𝑗̂ + 3𝑘 ̂ , 𝑣 = −𝑖̂ − 5 𝑘 ̂ y 𝑤⃗⃗ = 𝑖̂ − 3𝑗̂ + 4𝑘 ̂ de ℝ3, introduzca un paréntesis conveniente y resuelva las operaciones dadas a continuación: a. 𝑣 /𝑤⃗⃗ ∙ 𝑢⃗ b. 𝑢⃗ ∙ 𝑣 + 𝑤⃗⃗ c. 𝑣 𝑢⃗ ∙ 𝑤⃗⃗ d. 𝑣 ∙ 𝑤⃗⃗ × 𝑢

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Algebra
Dot Product
Cross Product
Vector Operations

Formulas

Dot product: 𝑢⃗ ∙ 𝑣⃗ = 𝑢₁𝑣₁ + 𝑢₂𝑣₂ + 𝑢₃𝑣₃
Cross product: 𝑢⃗ × 𝑣⃗ = |𝑖̂ 𝑗̂ 𝑘̂|
Sum of vectors: 𝑢⃗ + 𝑣⃗ = (𝑢₁ + 𝑣₁)𝑖̂ + (𝑢₂ + 𝑣₂)𝑗̂ + (𝑢₃ + 𝑣₃)𝑘̂

Theorems

Properties of Dot Product
Properties of Cross Product

Suitable Grade Level

Grades 11-12