The discussion revolves around the concept of skew lines in three-dimensional space and whether they can be considered perpendicular based on the properties of their direction vectors. Participants explore the relationship between the dot product of vectors representing the lines and the conditions for intersection.
Participants generally agree that perpendicular lines do not have to intersect if they are skew, but there is ongoing discussion about the implications of orthogonality in relation to intersection.
The discussion highlights the nuances in defining perpendicularity and intersection in three-dimensional space, particularly concerning skew lines and their direction vectors.
do you mean that in the case that x-axis is in its original position the x and y axes are perpendicular and intersect, and in the case that the x-axis is in y = 0, z = 1 the x and y axes are perpendicular and doesn't intersect ?RUber said:The lines would be considered orthogonal, but that does not imply that they intersect.
Consider the x and y axes. The intersect in the plane z=0. But if you raise the x-axis to y=0, z=1, it will never intersect the y-axis defined by x=0, z=0.
mohamed el teir said:do you mean that in the case that x-axis is in its original position the x and y axes are perpendicular and intersect, and in the case that the x-axis is in y = 0, z = 1 the x and y axes are perpendicular and doesn't intersect ?
yes sort of that, if lines with perpendicular directions but the lines themselves are skew, are they considered perpendicular or not, so they are perpendicular, thank youRUber said:Yes. That was your question, right? If orthogonal lines must intersect or not.