Mathematics

Problem

If in triangle

ABC

AB = \frac{\mathbf{u}}{|\mathbf{u}|} - \frac{\mathbf{v}}{|\mathbf{v}|}

and

AC = \frac{2\mathbf{u}}{|\mathbf{u}|}

, where

|\mathbf{u}| \neq |\mathbf{v}|

, then a.

1 + \cos 2A + \cos 2B + \cos 2C = 0

\sin A = \cos C

c. projection of

AC

BC

is equal to

BC

d. projection of

AB

BC

is equal to

AB