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
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