. Background Information:
I am studying linear algebra regarding vectors, planes, and lines.
. Logical Question:
How would you know if some vectors lie on a plane, or a line, or both?
. My Solution:
1. Vectors on the same plane:
Few vectors are on the same plane if they are linearly dependent, by testing Av1 + Bv2 + Cv3 = 0 or Av1 = -Bv2 - Cv3 (subtration of two other vectors yields one of the vectors); considering A, B, and C are not 0. Therefore, if the vectors are linearly dependent then they are on the same plane.
2. Vectors on the same line:
Few vectors are considered to be on the same line if they are scalar multiples of of one another. For example, v1 = 2v2 , v3 = 3v2.
Am I right? If you could confirm this for me it would be great.