Let \vec{a}, \vec{b} and \vec{c} be unit vectors lying on the same <strong>COPLANAR</strong> plane. What is \{(3\vec{a}+2\vec{b})\times(5\vec{a}-4\vec{c})\}\cdot(\vec{b}+2\vec{c}) equal to ?

Explanation

Because vectors \vec{a}, \vec{b}, and \vec{c} lie in the same plane, any vectors formed by their linear combinations are also coplanar. The expression represents a scalar triple product of three such coplanar vectors. The volume of a parallelepiped formed by coplanar vectors is zero.

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