Let the vectors $\vec{PQ}, \vec{QR}, \vec{RS}, \vec{ST}, \vec{TU}$ and $\vec{UP}$ represent the sides of a regular hexagon.
Statement-1: $\vec{PQ}× (\vec{RS}+\vec{ST}) ≠\vec 0$
Statement-2: $\vec{PQ}×\vec{RS} =\vec 0$ and $\vec{PQ}×\vec{ST} ≠\vec 0$
Answer & explanation
Correct answer: option 3
Clearly, $\vec{RS}+\vec{ST} =\vec{RT}$ which is not parallel to $\vec{PQ}$.
$∴\vec{PQ}× (\vec{RS}+\vec{ST}) ≠\vec 0$
So, statement-1 is true.
Also, $\vec{PQ}$ is not parallel to $\vec{RS}$.
$∴\vec{PQ}×\vec{RS} ≠\vec 0$
So, statement-2 is not true.