Given two different non-parallel vectors, a → and b → , prove that a → + b → and a → − b → are the bisector vectors of the angle formed by a → and b → .This question is in my book of vector geometry, but it is kind of weird for me. I do not know if I am approaching it the right way.I know that the formula for the angle bisector vector is given like this:Let u and v be vectors of non-zero length. Let ‖ u ‖ and ‖ v ‖ be their respective lengths. Then ‖ u ‖ v + ‖ v ‖ u is the angle bisector of u and v. So the only way a → + b → is the bisector vector is that both a → and b → have a length of one unit, but the question does not talk about this particular case, it seems phrased for all cases. Also I do not see how a → - b → could satisfy this formula.

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Given two different non-parallel vectors,             a      →       and             b      →      , prove that             a      →      +            b      →       and             a      →      −            b      →       are the bisector vectors of the angle formed by             a      →       and             b      →      .This question is in my book of vector geometry, but it is kind of weird for me. I do not know if I am approaching it the right way.I know that the formula for the angle bisector vector is given like this:Let   u and   v be vectors of non-zero length. Let   ‖  u  ‖ and   ‖  v  ‖ be their respective lengths. Then   ‖  u  ‖  v  +  ‖  v  ‖  u is the angle bisector of   u and   v. So the only way             a      →      +            b      →       is the bisector vector is that both             a      →       and             b      →        have a length of one unit, but the question does not talk about this particular case, it seems phrased for all cases. Also I do not see how             a      →       -            b      →        could satisfy this formula.

wietselau · Accepted Answer

A bit of geometry:In a Cartesian coordinate systemConsider             a      →        =                    A        B            →      ,             b      →        =                    B        C            →        ..Complete to form a parallelogram   A  B  C  D  .            a      →        +            b      →        =                    A        C            →      , a diagonal in the parallelogram .1)   ∠  C  A  B  =  ∠  D  C  B  :=  α, since   A  B      |        |    D  C.2)   ∠  C  A  D  =  ∠  A  C  B  :=  β, since   A  D      |        |    B  C.  △  A  B  C is isosceles , i.e.   α  =  β    ⟺        |        |                      A        B            →            |        |    =      |        |                      B        C            →            |        |  , i.e. they have the same length.

traquealwm · Accepted Answer

You are rigth, if you don&#039;t have equality hipothesis ∥u∥=∥v∥ the conclusion is false in general, you can draw any two vectors with diferent length and see difente angles.

Given two different non-parallel vectors, vec a and vec b, prove that vec a+vec b and vec a−vec b are the bisector vectors of the angle formed by vec a and vec b.

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