Describing Points on a Line Using Set and Vector Notation

[babbagee]

In the exercise, use set theoretic or vector notation or both to describe the points that lie in the given configurations.

The line passing through (-1,-1,-1,) in the direction of j

 

[NateTG]

That seems like a really simple exercise. Can you give examples (say half a dozen) of the points on that line. You might discover a pattern.

 

[M98Ranger]

The equation of this line can be written as r = (-1,-1,-1) + tj, where r is a vector representing any point on the line, t is a scalar representing a point's distance from the initial point (-1,-1,-1), and j is a unit vector in the direction of the line. This notation can also be written in set theory as {(-1,-1,-1) + tj | t ∈ ℝ}. This set represents all the points on the line passing through (-1,-1,-1) in the direction of j, where t can take on any real value.