- #1
HallsofIvy said:What is your question?
vela said:Your reasoning is correct, but you flipped a sign when calculating the dot product in your last step.
ehild said:Quite a lot of way to attack a problem... The distance between the skew lines is the length of the straight line which intersects both lines and is perpendicular to both of them. The tangent vector of this line is the vector product of
v1 and v2.
[tex]\vec n = \vec v_1\times \vec v_2[/tex]
The length of the perpendicular line segment is equal to the projection of any vector which connects a point on l1 to a point on l2, for example r12 that points from P1 to P2. The distance is
[tex]D=\frac{\vec n\cdot\vec r_{12}}{|\vec n|}[/tex]
ehild
The distance between two lines represents the shortest distance between any two points on the two lines. It is also known as the perpendicular distance, as it is the distance between two lines measured at a 90-degree angle.
The distance between two lines can be calculated by finding the distance between a point on one line and the nearest point on the other line. This can be done using the formula for finding the distance between a point and a line in a coordinate plane.
No, the distance between two lines is always a positive value. This is because it represents a physical distance, which cannot be negative.
The distance between two parallel lines is always the same, regardless of where it is measured. This is because parallel lines have the same slope and will never intersect, meaning the distance between them will never change.
The distance between two lines is influenced by the equations that represent them. Two lines with different equations will have different distances between them, while two lines with the same equation or equations that are parallel will have a distance of 0 between them.