Chapter 13 - Vector Geometry - 13.4 The Cross Product - Exercises - Page 676: 8

$1$

We calculate the determinant as follows: $$ \left|\begin{array}{rrr}{1} & {0} & {0} \\ {0} & {0} & {-1} \\ {0} & {1} & {0}\end{array}\right|=\left|\begin{array}{rrr} {0} & {-1} \\ {1} & {0}\end{array}\right|-0\left|\begin{array}{rrr} {0} & {-1} \\ {0} & {0}\end{array}\right|+0\left|\begin{array}{rrr} {0} & {0} \\ {0} & {1}\end{array}\right|=1. $$