If
\[
\vec r=2\hat i-\hat j+2\hat k,\qquad
\vec s=3\hat i-3\hat j+3\hat k,\qquad
\vec t=\hat i+2\hat j+\hat k
\]
are three vectors and \(\vec a\) is a vector such that
\[
\vec s\times\vec a=\vec r\times\vec a
\]
and
\[
\left|\vec t\times\vec a\right|=\sqrt{128},
\]
then \(|\vec t-\vec a|=\)
Show Hint
If
\[
\boxed{\vec u\times\vec v=\vec0,}
\]
then the vectors are parallel. Express one vector as a scalar multiple of the other before using the remaining conditions.