Math Problem Statement
2 vectors each of unit length which makes angle of 45 degree with ( 1, 0, 0) and are at right angles to ( 0, 0, 1) Create application based question
Solution
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Math Problem Analysis
Mathematical Concepts
3D Vectors
Dot Product
Cross Product
Unit Vectors
Formulas
Dot Product: A · B = |A| |B| cos(θ)
Cross Product: A × B = |A| |B| sin(θ) n̂
Unit Vector: v̂ = v / |v|
Theorems
Orthogonality Theorem: Two vectors are orthogonal if their dot product equals zero
Cosine Rule in Vector Geometry: Used to calculate the angle between two vectors
Suitable Grade Level
College-level (Physics, Engineering, or Advanced Mathematics)
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