00:01
They ask us to use the process from the previous problem to find the distance between two lines.
00:08
And again, i've written them in parametric form here.
00:15
So the directions, the directions each of these lines are in are these vectors here.
00:24
We need to find a normal to a line that's perpendicular to both of these.
00:33
And if there's perpendicular to both of those, we'll confine a plane such that these two lines lie in that plane, or are parallel to the plane anyway.
00:45
So take the cross product of these, and we get 11 minus 2 .14.
00:50
So we can define a plane that has this normal vector and also goes through the point, say this point on this line here.
01:03
So we can just pick a point on this line and make sure that that plane so that make sure that this line is in that plane so and if we make sure that this point is in the plane then that this thing has to be equal to three so our plane equation for our plane is given by this now we can pick a point on this other line here and let's just pick at this point here and t is zero and we can figure out okay if we plug this into here it's not gonna be so so we can write basically a function that looks like 11x minus 2y plus 14 z minus 3.
01:51
And that's a function of x, y, and z...