Math Problem Statement
Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) <2,1,2>
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Geometry
Direction Cosines
Direction Angles
3D Coordinate Systems
Formulas
Magnitude of a vector: |v| = sqrt(x^2 + y^2 + z^2)
Direction cosines: cos(α) = x/|v|, cos(β) = y/|v|, cos(γ) = z/|v|
Direction angles: α = cos^(-1)(x/|v|), β = cos^(-1)(y/|v|), γ = cos^(-1)(z/|v|)
Theorems
Trigonometric identities for cosines
Pythagorean theorem in 3D space
Suitable Grade Level
Grades 11-12 or early college
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