Math Problem Statement
what is the angle between (1,1,-1) and (0,2,3)
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Algebra
Dot Product
Angle Between Vectors
Formulas
Dot product formula: A · B = A_x B_x + A_y B_y + A_z B_z
Magnitude of a vector: |A| = sqrt(A_x^2 + A_y^2 + A_z^2)
Cosine of the angle between vectors: cos(θ) = (A · B) / (|A| |B|)
Theorems
Dot Product Theorem
Suitable Grade Level
Grades 10-12
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