In-class work for 7 June 2012
1.) Find the distance from the point $(4,-4,3)$ to the plane $2x-2y+5z+8=0$.

2.) Find the distance between the two parallel planes $x-5y-z=1$ and $5x-25y-5z=-3$.

3.) Consider the lines $\vec{r} = <1,2,3> + t<2,3,4>$ and $\vec{r} = <6,-7,4> + s<-1,4,1>$.

    a.) Find the point of intersection of the two lines.

    b.) Find an equation of the plane that contains both of these lines.

4.) Find a vector equation, parametric equation, and symmetric equation for the line passing through the point $(2,0,1)$ parallel to the vector $<1,-1,6>$.

5.) Find a vector equation of the line in which the planes $2x-5y+3z=12$ and $3x+4y-3z=6$ meet.

6.) Determine whether the lines $$L_1 : \frac{x-4}{2} = \frac{y+5}{4} = \frac{z-1}{3},$$ and $$L_2 : \frac{x-2}{1} = \frac{y+1}{3} = \frac{z}{2}$$ are parallel, skew, or intersecting. If they intersect, find the point of intersection.

7.) Find the distance from $(0,2,1)$ to the line $<1,1,1>+t<-2,1,3>$.

8.) Find the distance between the point $(1,2,3)$ and the plane $-3x+y-3z=4$.