\(\vec a,\vec b,\vec c\) are the position vectors of three points \(A,B,C\) respectively. If
\[
\angle ABC=\frac{\pi}{2},
\]
and
\[
\overrightarrow{AB}
=\hat{i}+4\hat{j}+(4-\lambda)\hat{k},
\qquad
\overrightarrow{AC}
=(\lambda-1)\hat{i}+6\hat{j}+(2-\lambda)\hat{k},
\]
then \(\lambda=\)
Show Hint
If the angle between two vectors is \(90^\circ\), then
\[
\boxed{\vec u\cdot\vec v=0.}
\]
Always form the vectors from the vertex of the given angle before taking the dot product.