How do you determine the angle between two vectors using their direction cosines?

To determine the angle between two vectors using their direction cosines, use the formula cos(θ) = l₁l₂ + m₁m₂ + n₁n₂, where l₁, m₁, n₁ are the direction cosines of the first vector and l₂, m₂, n₂ are the direction cosines of the second vector.

The angle θ between two vectors can be calculated by taking the dot product of their direction cosines. The direction cosines represent the cosines of the angles between each vector and the coordinate axes. The formula cos(θ) = l₁l₂ + m₁m₂ + n₁n₂ effectively combines these components to find the cosine of the angle between the two vectors.