Math Problem Statement
u = -4j + 6k v = -3i + j + 5k find the angle between them
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Algebra
Dot Product
Angle Between Vectors
Formulas
cos(θ) = (u · v) / (||u|| ||v||)
Dot product: u · v = (u_i * v_i) + (u_j * v_j) + (u_k * v_k)
Magnitude: ||a|| = √(a_i^2 + a_j^2 + a_k^2)
Theorems
Cosine of the angle between two vectors
Suitable Grade Level
Grades 11-12
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