Formulate a general method for finding the distance between two skew (i.e., non intersecting) line in space. (Hint: the shortest line segment joining the two skew lines will be perpendicular to both of them).
distance between skew lines
and you will see various discussions and videos on the topic.
working
To find the distance between two skew lines in space, you can follow these steps:
Step 1: Identify two points, one on each line.
Select a point on one line and label it as Point A. Similarly, choose a point on the other line and label it as Point B. These points will help us determine the direction vectors of the lines.
Step 2: Determine the direction vectors of the lines.
Find the direction vector for each line. To do this, subtract the coordinates of Point A from a second point on the same line. Repeat this process for the other line, subtracting the coordinates of Point B from a second point on that line. Now you have two direction vectors, one for each line.
Step 3: Calculate the cross product of the direction vectors.
Take the cross product of the two direction vectors. The result will give you a vector that is perpendicular to both lines. Let's call this vector C.
Step 4: Determine a point on the shortest line segment.
To find a point on the shortest line segment connecting the two skew lines, you will need to use the position vectors of Point A or Point B.
Step 5: Calculate the shortest distance.
Use the formula for the distance between a point and a line to find the shortest distance. The formula is:
Distance = |AC dot C| / |C|
Here, C is the vector obtained from the cross product of the direction vectors, and AC is the vector from the point on the line to the point you calculated in Step 4.
By following these steps, you can find the distance between the two skew lines in space.