Thomas' Calculus 13th Edition

$a=10.$
The cross product of parallel vectors is the zero vector. ${\bf (2i+4j-5k)}\times{\bf (-4i-8j+ak)}=\left|\begin{array}{rrr} {\bf i} & {\bf j} & {\bf k}\\ 2 & 4 & -5\\ -4 & -8 & a \end{array}\right|$ $=(4a-40){\bf i}-(2a-20){\bf j}+(16-16){\bf k}$ For this to be the zero vector, it must be that $\left\{\begin{array}{l} 4a-40=0\\ 2a-20=0 \end{array}\right.$ that is, $a=10.$