Math Problem Statement

Let
→ a

⟨ 0 , 2 , − 3 ⟩ and
→ b

⟨ 1 , − 3 , 5 ⟩ .

Find the angle between the vector (in radians)

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Algebra
Dot Product
Trigonometry

Formulas

Dot Product: a · b = a₁b₁ + a₂b₂ + a₃b₃
Magnitude of a Vector: |a| = √(a₁² + a₂² + a₃²)
Cosine of the Angle Between Two Vectors: cos(θ) = (a · b) / (|a| * |b|)

Theorems

Cosine Rule for Vectors

Suitable Grade Level

Grades 10-12