Answer
(a) $-2$
(b) No, 2.
Work Step by Step
(a) Given the three vectors, first calculate the cross product of the two vectors: $\vec v\times\vec w
=(-1\times1-1\times1)i+ (1\times1-0\times1)j+ (0\times1+1\times1)k =-2i+ j +k$. Next we calculate the scalar triple product as $\vec u\cdot(\vec v\times\vec w)=1\times(-2)-1\times1+1\times1=-2$
(b) As the scalar triple product is not zero, we conclude that these vectors are not coplanar, and the volume of the parallelepiped is 2.
