distance between 2 skew lines
versus actually finding the two closest 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NiI=Stewart Calculus 9e. 12.5.78. Find the distance between these 2 skew 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make Maple functions out of them.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We separate out the position vector and orientation vector for each line.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 nonzero cross product gives us a normal to the pair of parallel planes they determine.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Project the difference vector of any two points on the two lines (set parameters to zero) along the unit normal to get the distance up to sign.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVElbmhhdEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkmbWZyYWNHRiQ2KC1GLDYlUSJuRidGL0YyLUYjNictRiw2I1EhRictRiM2JUZXLUkmbXNxcnRHRiQ2Iy1GIzYmRlItRjY2LVEpJm1pZGRvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMTY2NjY2N2VtRicvRk5GX29GUkY5RjlGV0YvRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmZvLyUpYmV2ZWxsZWRHRj0vJStleGVjdXRhYmxlR0Y9Rjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWZlbmNlZEdGJDYkLUYjNictRiw2JVEjcjFGJ0YvRjItRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZlbi1GLDYlUSNyMkYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5LUY2Ni1RKSZtaWRkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjE2NjY2NjdlbUYnL0ZORmBvLUYsNiVRJW5oYXRGJ0YvRjJGam5GOQ==minimum separation distance determines the actual closest pointsTo actually find which points are closest, we need to solve a 2d minimum problem, minimizing the square of the separating distance between the two lines as a function of their two parameters, setting the derivative wrt each independent variable to zero to find the unique global minimum of the distance function which we know must exist.We will study multidimensional max-min problems later, but it amounts to setting each independent derivative to zero to find the critical points, then checking for global max-min. In our case we know there is a unique global minimum distance between the two skew lines.
Unfortunately to avoid complex dot product complications we need a real dot product here.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Plugging back in finds the two closest points, which we can then illustrate graphically.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 plot the connecting line segment and the points themselves.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Now we show a piece of each line symmetrically about the nearest points (shown in green below), adjusting the range by eye so that they are both about the same.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 that these two lines are nearly parallel. Rotate them around.
However, the original two points were far away from the closest points. We plot the spacecurves from the zero parameter values showing those original points in blue.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To compare the angle between the orientations of the two lines, the next plot shows vectors aligned with the two lines at each of the nearest points, but the small angle between the lines makes it not a very nice illustration.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=orthogonal connecting vector does it! [clever soln]So one of my students who brought up this question in the first place took an approach that does not require max-min methods. The difference vector between the two curves should be orthogonal to both, namely it should point along the normal to the pair of parallel planes they determine containing them, so it should be proportional to that normal (let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn be the proportionality factor). This next equation sets the difference vector to a multiple of the normal, then we solve the three equations for the three parameters.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 the two nearest points are: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 agree with our previous solutions!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 moral of the story is that different people see things in different ways, so it is important to collaborate in solving problems.better example for plotting geometryThese lines are nearly parallel so not making very nice plots. We can make up a better example.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 for the plot.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Find the nearest points.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Plugging back in finds the two closest points, which we can then illustrate graphically.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 plot the minimal connecting line segment and the points themselves.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Next the two skew lines.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Finally we place both line direction vectors at each of the nearest points, and include the two parallel planes.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Next we put in the original points and their separation vector.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 it around to get a sense of the situation.TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDc5NTUxOTMyWColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiJGKSIiIUYlTTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDc5NTUzNjEyWColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiIiIiYhIiNGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDc5NTQ2OTk2WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiIiIiciIiNGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDc5NTQ4NTU2WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIiMiIzoiIidGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDc5NTQzNjIwWColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiIichIiMiIiRGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDc5NTQxNjg0WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQjIiInIiIoIyEiI0YrIyIiJEYrRiU=TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDk5MzY2NTY0WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQjIiNeIiIoIyIkciNGKyMiIykpRitGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDk5MzYwMDY4WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQjIiNSIiIoIyIkdiNGKyMiIyMpRitGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDk5MzYxNjI4WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQjIiNeIiIoIyIkciNGKyMiIykpRitGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDkwNTU5MDk5MzYyOTQ4WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQjIiNSIiIoIyIkdiNGKyMiIyMpRitGJQ==