Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Magnitude
Dot Product
Angle Between Vectors
Cross Product
Formulas
Magnitude: |v| = √(vx² + vy²)
Dot Product: v1 ⋅ v2 = v1x * v2x + v1y * v2y
Angle: cos(θ) = (v1 ⋅ v2) / (|v1| * |v2|)
Cross Product: v1 × v2 = (v1x * v2y - v1y * v2x)k̂
Magnitude of Cross Product: |v1 × v2| = |v1| * |v2| * sin(θ)
Theorems
Dot Product Theorem
Cross Product in 2D Vectors
Suitable Grade Level
Undergraduate Level