question_answer

Let the vectors \[\overrightarrow{PQ},\]\[\overrightarrow{QR,}\]\[\overrightarrow{RS,}\]\[\overrightarrow{ST,}\]\[\overrightarrow{TU,}\]and \[\overrightarrow{UP}\] represent the sides of a regular hexagon.

Statement 1: \[\overrightarrow{PQ}\times (\overrightarrow{RS}+\overrightarrow{ST})\ne \overrightarrow{0}\] because

Statement 2: \[\overrightarrow{PQ}\times \overrightarrow{RS}=\overrightarrow{0}\] and \[\overrightarrow{PQ}\times \overrightarrow{ST}\ne \overrightarrow{0}\]

A)  Statement-1 is True, Statement-2 is True; Statement-2 is the correct explanation for Statement-1

B)  Statement-1 is True, Statement-2 is True; Statement-2 is not the correct explanation for Statement-1

C)  Statement-1 is True, Statement-2 is False

D)  Statement-1 is False, Statement-2 is True

E)  None of these