Let the vectors −−→PQ,−−→QR,−−→RS,−→ST,−−→TU and −−→UP represent the sides of a regular hexagon.
Statement - 1: −−→PQ×(−−→RS+−→ST)≠0
Statement - 2: −−→PQ×−−→RS=0 and −−→PQ×−→ST≠0
A
Statement −1 is True, Statement −2 is True; Statement −2 is the correct explanation of Statement −1.
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B
Statement −1 is True, Statement −2 is True; Statement −2 is the incorrect explanation of Statement −1.
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C
Statement −1 is True, Statement −2 is False.
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D
Statement −1 is False, Statement −2 is True.
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Solution
The correct option is C Statement −1 is True, Statement −2 is False.
We have −−→RS+−→ST=−−→RT. As −−→PQ and −−→TR are not parallel to each other, ⇒−−→PQ×(−−→RS+−→ST)=−−→PQ×−−→RT≠0.
Thus Statement -1 is true.
Since −−→PQ and −−→RS are not parallel, −−→PQ×−−→RS≠0.
But −−→PQ and −→ST are parallel to each other ⇒−−→PQ×−→ST=0
Therefore, the Statement -2 is false.