alleryIf $vec{a}$, $vec{b}$ and $vec{c}$ are coplanar, then the scalar triple product satisfies
A$\vec{a}\cdot(\vec{b}\times\vec{c})=1$
B$\vec{a}\cdot(\vec{b}\times\vec{c})=-1$
C$\vec{a}\cdot(\vec{b}\times\vec{c})=0$
D$\vec{a}\cdot(\vec{b}\times\vec{c})=|\vec{a}||\vec{b}||\vec{c}|$
Answer & Solution
Correct answer: C. $\vec{a}\cdot(\vec{b}\times\vec{c})=0$
The scalar triple product gives the signed volume of the parallelepiped formed by the three vectors.
If the vectors are coplanar, that volume is zero, so $\vec{a}\cdot(\vec{b}\times\vec{c})=0$.
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