Mathematics

Problem

For two non-zero, non-collinear vectors

\vec A

and

\vec B

, the bisector of the angle between them is defined as the direction that makes equal angles with

\vec A

and

\vec B

. a. (i) Derive an expression for a vector

\vec D

that lies along the bisector of the angle between

\vec A

and

\vec B

in terms of

\vec A

and

\vec B

. Clearly obtain the corresponding unit vector. b. (ii) Using your result from part (i), find the unit vector along the angle bisector for

\vec A = 3\,\hat i + 4\,\hat j

and

\vec B = 4\,\hat i + 3\,\hat j

. c. (iii) Show that the unit vector you obtained in part (ii) indeed makes equal angles with

\vec A

and

\vec B

by calculating the required scalar products.