Problems

01

Planes intersection line, parametric

Find a parametric equation for the line formed as the intersection of the two planes $6x-3y+z-5=0$ and $-x+y+5z-5=0$. What is the angle between these planes?

02

Plane perpendicular, two scalar planes

Find a plane that is perpendicular to the two planes given by $x+y-3=0$ and $x+2y-z-4=0$, respectively.

03

Distance point to line

Compute the distance from the point $\mathbf{p}=(1,5,-2)$ to the line given by $\mathbf{r}(t)=(-2,3,1)+t(4,0,-1)$.

Repeat the problem for $\mathbf{p}=(-2,1,3)$ and $\mathbf{r}(t)=(1,2,0)+t(-1,1,-2)$.

04

Distance between skew lines

Find a general formula for the distance between two skew lines, i.e. lines in space which are not parallel and do not intersect. (Assume they are given parametrically in vector form.)