Question

If a variable line in two adjacent positions has direction cosines (l, m, n) and (l + δl, m + δm,n + δn), show that the small angle δθ between the two positions is given by (δθ)² = (δl)² + (δm)² + (δn)².

Answer 1

We have,

l² + m² + n² = 1 

Now, δθ be the angle between two positions.