Consider the following statements: I. For any three vectors \overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}; \overrightarrow{a} \cdot[(\overrightarrow{b}+\overrightarrow{c}) \times(\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})]=0 II. For any three coplanar unit vectors \overrightarrow{d}, \overrightarrow{e}, \overrightarrow{f} ;(\overrightarrow{d} \times \overrightarrow{e}) \cdot \overrightarrow{f}=1 Which of the statements given above is/are correct?

Correct Answer is : Both I and II

UPSC NDA I 2010 Mathematics Paper

Question : 34 of 120

Marks: +1, -0

Consider the following statements:
I. For any three vectors

→

;

→

⋅[(

→

)×(

→

)]=0
II. For any three coplanar unit vectors

→

;(

→

)⋅

→

=1
Which of the statements given above is/are correct?

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