Question

If the vector i+j+k bisects the angles between the vector c and the vector 3i+4j then the unit vector in the direction if c is

Answer 1

Well, what you’ve got to try to do first is find the unit vectors corresponding to the a and b.

unit vector of a=(3i-4k)/5

unit vector of b=(5j+12k)/13

Diagonals of a rhombus bisect its angles and as you can see, the unit vectors a and b act as diagonals of a rhombus and by adding them, you can find the vector c which acts as an angular bisector for vectors a and b. The basic principle is that you need equal vectors to say that bisector of a and b= a+b.

c=(3/5)i+(5/13)j+(8/65)k