What is the shortest distance between the skew lines $L_1:\mathbf{r}=(1,0,0)+t(1,1,0)$ and $L_2:\mathbf{r}=(0,1,1)+s(0,1,1)$?
Question 2
Which expression gives the volume $V$ of the parallelepiped formed by vectors $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$?
Question 3
Which is the Cartesian equation of the plane perpendicular to the line with direction vector $\mathbf{d}=(2,1,-3)$ and passing through the point $P(1,-2,0)$?
Question 4
What is the acute angle between the planes $2x-3y+z=5$ and $x+y-2z=3$?
Question 5
What are the coordinates of the foot of the perpendicular from $P(1,0,0)$ to the plane $x+2y+2z-5=0$?
