Chapter 5 - Inner Product Spaces - 5.5 Applications of Inner Product Spaces - 5.5 Exercises - Page 282: 39

$1$

We know that $ai+bj+ck=(a,b,c).$ We know from earlier that if two adjacent vectors forming the sides of a parallelogram are $u$ and $v$, then the area can be computed by $A=u\cdot v$. Hence, here $A=(0,1,0)(0,1,1)=0+1+0=1$