The problem involves determining the conditions under which the vectors a = [2, 2, 2], b = [3, 0, 1], and an unknown vector c are linearly dependent. The original poster is exploring the concept of linear dependence and the use of the dot product and triple product in this context.
Participants are actively discussing various approaches to express the vector c in terms of other parameters. There is a suggestion to consider c as a linear combination of vectors a and b, indicating a productive direction in the exploration of linear dependence.
There is an implicit assumption that the vectors a and b are linearly independent, which influences the discussion about the form of vector c. The participants are navigating through the constraints of the problem without reaching a definitive conclusion.
tweety24 said:okay sweet, thank you! =)
Not really, I'm not sure how it would work the other way without the triple product.
What Dick is suggesting here is the simplest, most straightforward approach. If you want to find all vectors c so that {a, b, c} is a linearly dependent set, and you can tell by inspection that a and b are linearly independent, then c must be a linear combination of a and b. This is exactly what Dick's equation represents.Dick said:How about c=s*[2, 2, 2]+t*[3, 0, 1]?