## 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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