Thread: Vector-Valued Lines

Urgent! Please help soon! Here's the equation:

Find the distance between the lines:

r1(t) = (1,2,3) + t(0,-1,2)
r2(t) = (0,1,1) + t(1,1,0)

So far all I've been able to figure out is conversions to unit vector i, j, and k:

r1(t) = 0i + 1 -j +2 +2k +3 = -j + 2k + 6
r2(t) = i + j + 1

But here I hit a block....please help!

Hey nrr5094.

You need to find a vector which is perpendicular to both lines (Hint: think about the cross product of the directional vectors of each line)

Originally Posted by nrr5094

Find the distance between the lines:
r1(t) = (1,2,3) + t(0,-1,2)
r2(t) = (0,1,1) + t(1,1,0)

If the two lines are are parallel chose a point on one of them and then find the distance of it to the other line.

In general, let say two lines then