If
\[
|\vec a|=3,\qquad |\vec b|=4
\]
and the angle between \(\vec a\) and \(\vec b\) is
\[
\frac{\pi}{6},
\]
then
\[
\left|(4\vec a+\vec b)\times(\vec a-3\vec b)\right|
=
\]
Show Hint
For cross-product expressions involving linear combinations, expand first and immediately use
\[
\vec a\times\vec a=0,
\qquad
\vec b\times\vec b=0,
\qquad
\vec b\times\vec a=-\vec a\times\vec b.
\]
This often reduces the entire expression to a single multiple of \(\vec a\times\vec b\).