If 
, where 
, 
and 
are all non-zero vectors, show that bisects the angle between and .
You may consider the scalar product of and , and and .
Let 
be the angle between and .
Let 
be the angle between and .
(Our goal is to show that 
.)
— (1)
— (2)
Using (1), we have
Using (2), we have
Since 
, then the parallelogram with sides determined by vectors 
and 
is a rhombus and corresponds to its diagonal. But a diagonal of a rhombus bisects its angle: the obtained two triangles are congruent by SSS. Clearly the same argument gives a more general statement: the sum of two vectors of equal length bisects the angle between them.
9758 A-level A-levels A'levels application H2 Mathematics How To Mathematics Pure Mathematics Scalar Product Vectors
Vectors Question #22017-02-272017-03-01http://theculture.sg/wp-content/uploads/2018/03/the-culture-logo.pngThe Culture SGhttp://theculture.sg/wp-content/uploads/2016/10/yvl081tvnva-worthy-of-elegance.jpg200px200px
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