Practicing Success
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 $\vec{PQ}×\vec{ST}≠\vec 0$ |
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1. Statement-1 is True, Statement-2 is False. Statement-1 is False, Statement-2 is True. |
Statement-1 is True, Statement-2 is False. |
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. |