# Chapter 12 - Vectors and the Geometry of Space - 12.4 The Cross Product - 12.4 Exercises - Page 862: 34

$1$

#### Work Step by Step

$a=i+j=\lt 1,1,0\gt$ $b=j+k=\lt 0,1,1\gt$ $a=i+j+k=\lt 1,1,1\gt$ Volume of a parallelepiped is defined as: $V=|a \cdot (b \times c)|$ $b \times c= \lt 0,1,1 \gt \times \lt 1,1,1 \gt=\lt 0,1,-1 \gt$ $|a \cdot (b \times c)|= |\lt 1,1,0 \gt \cdot \lt 0,1,-1 \gt|$ $=|1 \cdot 0+1 \cdot 1+ 0 \cdot (-1)|$ $=|1|$ $=1$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.