# Linear algebra. Take 2!

dangish
I already posted this once, have a hard time believing nobody knows how to do it, and it's due tomorrow, so here it is again:

Find the distance between the nonparallel lines,

L1:

|x| ...|4| .....|1|
|y| = |-1| + t|0|
|x| ...|3| ....|2|

and L2:

|x| ...|1| .....|-3|
|y| = |2| + s|1|
|x| ...|2| ....|-1|

picture the above as matricies, sorry i dont know how to properly make them :...(

Attempt at a solution:

The hint told me to find a vector orthogonal to both lines. so i took the normal vector of each line ( the three numbers after s and t ) and got a vector parallel to each.

The vector I used was v = |6,15,-3| <-- again picture this as a matricie.

The next part in the hint said take a plane with this normal containing one of the lines.

so I did and got, 6x +15y - 3z = d , then I subbed in a point from L2 to get,

6(1)+15(2)-3(2)=d ==> d=30

the equation of the plane is now 6x+15y-3z=30

The next part of the hint says "use a projection", and this is where I am stuck.

how will I project the line onto the plane? any help would be much appreciated, thanks.