Statement 1: The vectors a, b and c lie in the same plane if and only if a( b c)=0.

Question

Statement 1: The vectors $\vec a,\vec b$ and $\vec c$ lie in the same plane if and only if $\vec a\cdot(\vec b	imes\vec c)=0$.

Statement 2: The vectors $\vec u$ and $\vec v$ are perpendicular if and only if $\vec u\cdot\vec v=0$, where $\vec u	imes\vec v$ is a vector perpendicular to the plane of $\vec u$ and $\vec v$.

Accepted Answer

Statement 1 is the standard necessary and sufficient condition for coplanarity, so it is true. Statement 2 as phrased is not a valid/true statement (perpendicularity of $\vec u,\vec v$ is unrelated to the direction of $\vec u	imes\vec v$ in the manner described), so it is false.

Solutions · 1