True or false? Let vec(u) and vec(w) two vectors. Then vec(w) −1/2 vec(u) and 2 vec(w) − vec(u⃗) are perpendicular.

traffig75 2022-09-17 Answered
Is it true that ( w 1 2 u ) ( 2 w u ) u , w ?
I think is false. Let u = ( 1 , 0 , 0 ) and w = ( 0 , 1 , 0 ) two vectors. Then
( w 1 2 u ) ( 2 w u ) = ( 1 2 , 1 , 0 ) ( 1 , 2 , 0 ) = 1 2 + 2 = 5 2 0.
Is it correct?
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Answers (1)

Karli Moreno
Answered 2022-09-18 Author has 2 answers
They are parallel
( 2 w u ) = 2 ( w 1 2 u )
this shows one is a factor of the another.
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