You are not logged in.
Pages: 1
Thanks.
I understand what you say. But I also see that you don't see what I see.
Since the question is related to the basics of vectors, I might try posing the problem in a different fashion.
When do we say two given vectors linearly independent? OR,
Do two arbitrarily chosen intersecting vectors form a pair of linearly independent vectros?
To me, there appears a paradox and I sought help. If you don't see it, it is ok. But if you see it any time and if you have a solution, please let me know.
Thanks.
Thanks again
We can consider the example given by you with a modification of one of the vectors, say, the vector b(2). So, the three values for 'a' and 3 for 'b' are:
a(1) = (2,1)
a(2) = (4,4)
b(1) = (4,2)
b(2) = (6,6)
Thanks again.
F = ∑F(i) = m(i)a(i) =0, is an example where a triplet of F(i)s forms a triangle, but the corresponding triplet of a(i)s doesn't, unless m(i) = constant. The parallelogram law of addition of force vectors doesn't demand m(i) to be constant for its validity. F is force, m is mass on which the force acts producing an acceleration a. F and a are like parallel vectors.
Triplet of vectors is just three vectors.
Thank you for the reply.
The solution implicitely demands that the ratios of magnitudes of the corresponding vectors a(i) and b(i), be a constant (When such is the case, it is evident that we can always form two similar triangles with the vector triplets). But no such demand is imposed in the statement of the problem.
Therefore, the issue is: Is it possible to form similar triangles with the two vector triplets a(i) and b(i) such that a(i), b(i) are like parallel vectors, a(i) triplet forms a triangle and where the ratios of the magnitudes of the corresponding vectors is not a constant?
If a(i) and b(i) represent like parallel vectors, and a triplet of a(i) forms a triangle, then does the corresponding triplet of b(i) also form a similar triangle? If it does not, does it lead to a paradox?
When do we say two straight lines are linearly independent? When do we say two vectors are linearly independent?
Are the sides of a triangle lenearly independent quantities?
Pages: 1