Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Inner product space
Orthonormal basis
Vector projection
Angle between vectors

Formulas

Inner product: ⟨u, v⟩ = u1*v1 + u2*v2 + u3*v3
Norm of a vector: ||u|| = √(⟨u, u⟩)
Projection: u_parallel = (⟨u, v⟩ / ⟨v, v⟩) * v
Angle between vectors: cos(θ) = ⟨u, v⟩ / (||u|| * ||v||)

Theorems

Properties of orthonormal bases
Pythagoras theorem for norms

Suitable Grade Level

Undergraduate Level (First or second year)