Three Dimensional Geometry

Let $l_1$ be the line joining $(1, 1, 1)$ and $(3, 1, 3)$ and let $l_2$ be the line joining $(0, 2, -1)$ and $(2, 0, 3)$. What is the angle between $l_1$ and $l_2$?

Consider the lines $L_1$ and $L_2$ given below:
$$ \begin{gathered} L 1: x=2+\lambda, y=3+2 \lambda, z=4+3 \lambda \\ L 2: x=4+\lambda, y=4, z=4+\lambda \end{gathered} $$
If $(2,3,4)$ is the point of $L_1$ that is closest to $L_2$, then whi...

Let $L$ be a straight line passing through the origin, and it makes angles $\alpha, \beta$ and $\gamma$ with the positive $X, Y$ and $Z$-axes, respectively. What is the value of $\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma$ ?