Question

Find the distance between the skew lines with parametric equations x = 3 + t, y = 3 + 6t, z = 2t, and x = 2 + 2s,y = 5 + 15s, z = −3 + 6s.?

Answer 1

Step 1:

The parametric equations of the skew lines are considered as,

Since two lines are skew lines they can be considered as lying on two parallel planes .

Find the plane equation and choose any point on line , then find the distance between them.

It is same as the distance between the skew lines.

The vectors parallel to the skew lines are

The normal vector to the vectors is .

The normal vector to the vectors is

Answer 2

Continued:

Step 2:

Find the point on line by putting in parametric equation of .

The point on the line is .

Plane equation with normal vector is .

Find the plane equation by substituting and in above formula.

Find the point on the line by substituting in parametric equation of .

The point on the line is .

Formula for the distance from a point to the plane is .

Find the distance from  the point to the plane using above formula.

Solution:

The distance between the skew lines is .