Question is in the attachment. Please open the attachment. Thank you.
The file is pretty messed up, but I think I got the question.
(I changed the condition on k because the problem statement was not correct. k need not be negative.)Code:If two vectors and have the property that then there exists a scalar such that
By definition:
where is the angle between the two vectors.
So the problem statement:
means that
which means that = 0 or 180 degrees. Thus the vectors are parallel or antiparallel.
Vectors which are parallel (or antiparallel) are the same vector, up to a rescaling, ie. there exists a scalar k (which just changes the length of the vector) such that . (k is positive if the vectors are parallel and negative if they are antiparallel.)
-Dan
Hi Dan ,
Thank you very much for your reply. I tried to type the quetion into Word, unfortunately , it is not working properly.
Let me type the question again.
Question
If U*V = - IUI * IVI , and U and V are nonzero, then there exist a scalar k < 0 such that U = K*V .
Note: U and V are vectors.
The answer is TRUE.
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Here is what I can conclude so far:
If alpha is the angle between U and V , then cos alpha must = -1.
So alpha must = pi.
which implies that U and V point in the opposite directions.
My question is :
Is there existing a scalar K < 0 such that U = K*V when U and V point in the opposite directions?
I think the answer is Yes. K must be negative since they are pointing in the opposite directions.
Please let me know if I am wrong.