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Mar 22, 2011 · Given two lines joining A,B and C, D in 3D how do I figure out if they intersect, where they intersect and the ratio along AB at which the intersection happens? I can quite hapilly work out the equation for the lines in different forms. I'm guessing that you need to change them to parametric form, equate the equations and do some algebra ...
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Aug 17, 2024 · Given two lines in the two-dimensional plane, the lines are equal, they are parallel but not equal, or they intersect in a single point. In three dimensions, a fourth case is possible. If two lines in space are not parallel, but do not intersect, then the lines are said to be skew lines (Figure \(\PageIndex{5}\)).
To determine if two lines intersect, set them equal and solve: intersection occurs where p 1 + a 1 * v 1 = p 2 + a 2 * v 2 (note that there are two unknowns, a 1 and a 2 , and two equations, since the p 's and v 's are multi-dimensional)
Dec 21, 2020 · So we need a vector parallel to the line of intersection of the given planes. For this, it suffices to know two points on the line. To find two points on this line, we must find two points that are simultaneously on the two planes, \(x-z=1\) and \(y+2z=3\). Any point on both planes will satisfy \(x-z=1\) and \(y+2z=3\).
Oct 11, 2024 · No, two non-parallel lines in 3D space generally do not intersect. Such lines are called skew lines, and they do not lie in the same plane. In fact, two lines in 3D space can be: Intersecting at exactly one point; Parallel to each other (but not identical); Identical (and therefore also parallel); or; Skew (neither parallel nor intersecting).
- Anna Szczepanek
Therefore we need a vector parallel to the line of intersection of the given planes. For this, it suffices to know two points on the line. To find two points on this line, we must find two points that are simultaneously on the two planes, \(x-z=1\) and \(y+2z=3\text{.}\) Any point on both planes will satisfy \(x-z=1\) and \(y+2z=3\text{.}\)
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Feb 7, 2023 · (a) Two distinct lines in 3D space are either parallel or intersecting. (b) Three planes may all intersect in a point or not at all, but they can’t all intersect in a line. (2) (textbook 12.5.71) Find the distance from the point (1; 2;4) to the plane 3x+ 2y + 6z = 5. (3) (textbook 12.5.9) Find parametric equations and symmetric equations for ...
