Math Problem Statement
Solve a and b when a=3i-4j+2k and b = -i + 2j-3k
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Algebra
Dot Product
Cross Product
Vector Magnitude
Angle Between Vectors
Formulas
Magnitude of vector |v| = sqrt(x^2 + y^2 + z^2)
Dot product a · b = ax * bx + ay * by + az * bz
Cross product a × b = determinant of the matrix with unit vectors i, j, k and the components of a and b
Angle θ between vectors: cos θ = (a · b) / (|a| |b|)
Theorems
Pythagorean Theorem for vector magnitude
Dot Product and Cross Product Theorems
Suitable Grade Level
Grades 11-12