1. **Problem Statement:** Given that $l^2 + m^2 + n^2 = 1$ and $l'^2 + m'^2 + n'^2 = 1$, find the value of $ll' + mm' + nn'$. 2. **Formula and Explanation:** The expressions $l^2 + m^2 + n^2 = 1$ and $l'^2 + m'^2 + n'^2 = 1$ indicate that the vectors $\mathbf{v} = (l, m, n)$ and $\mathbf{v'} = (l', m', n')$ are unit vectors. The value $ll' + mm' + nn'$ is the dot product $\mathbf{v} \cdot \mathbf{v'}$. 3. **Important Rule:** The dot product of two unit vectors satisfies the inequality $$-1 \leq \mathbf{v} \cdot \mathbf{v'} \leq 1$$ because the dot product equals $|\mathbf{v}||\mathbf{v'}|\cos\theta = \cos\theta$ where $\theta$ is the angle between the vectors. 4. **Intermediate Work:** Since both vectors are unit vectors, $$ll' + mm' + nn' = \cos\theta$$ where $\theta$ is the angle between the vectors. 5. **Conclusion:** The value of $ll' + mm' + nn'$ is always less than or equal to 1. Hence, the correct choice is (c) is always less than or equal to 1.