If the vectors and represent the sides of a regular hexagon. Then, Statement I. because Statement II. and .
Statement I is correct; Statement II is incorrect
Explanation for the correct option :
Checking both the statements,
The six sides of a regular hexagon is represented by vectors as and it can be shown as:
Now the statement I is.
The left hand side of the statement can be split as:
Now, vectors and are not parallel so , so the first term is not equal to zero.
The vectors and are parallel so , so the second term is equal to zero.
So overall the expression is not equal to zero. So the statement is true.
It is already shown that and , so the statement II stating that and is false.
Thus, the first statement is correct and the second statement is incorrect.
Hence, the correct option is C.