Three Vectors A, B, and C Are Given $\mathbf { a } \cdot ( \mathbf { b } \times \mathbf { c } )$

Short Answer

Three vectors a, b, and c are given.
(a) Find their scalar triple product
$\mathbf { a } \cdot ( \mathbf { b } \times \mathbf { c } )$ .
(b) Are the vectors coplanar? If not, find the volume of the parallelepiped that they determine.
$\mathbf { a } = \langle 3,0 , - 4 \rangle , \mathbf { b } = \langle 2,2,2 \rangle , \mathbf { c } = \langle 7,4,0 \rangle$