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