Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Algebra
Parametric Equations
Planes in 3D
Formulas
Direction vector of a line: \langle dx/dt, dy/dt, dz/dt \rangle
Cross product of vectors: \mathbf{v_1} \times \mathbf{v_2}
Equation of a plane: a(x - x0) + b(y - y0) + c(z - z0) = 0
Theorems
Two lines are parallel if their direction vectors are scalar multiples
Cross product gives a normal vector to a plane
Suitable Grade Level
Undergraduate level or advanced high school math
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