Answer
(a) $0$
(b) Yes.
Work Step by Step
(a) Given the three vectors, first calculate the cross product of the two vectors: $\vec v\times\vec w
=\langle (1\times0-1\times4), (1\times7-1\times0), (1\times4-1\times7) \rangle
=\langle -4, 7, -3 \rangle$. Next we calculate the scalar triple product as $\vec u\cdot(\vec v\times\vec w)
=3\times(-4)+0\times7-4\times(-3)=0$
(b) As the scalar triple product is zero, we conclude that these vectors are coplanar.
