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 SGhttps://theculture.sg/wp-content/uploads/2016/10/yvl081tvnva-worthy-of-elegance.jpg200px200px
About
KS TengKS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.