If the vector
\[
\alpha\hat i+\beta\hat j+\hat k
\]
is along the bisector of the angle between the vectors
\[
2\hat i-\hat j+2\hat k
\]
and
\[
\hat i+2\hat j+2\hat k,
\]
then \(2\alpha+6\beta=\)
Show Hint
The internal bisector direction between vectors \(\vec a\) and \(\vec b\) is
\[
\frac{\vec a}{|\vec a|}+\frac{\vec b}{|\vec b|}.
\]
Always normalize before adding.