109.ABCDEF is a regular hexagon with point O as centre.The value of (AB vector + AC vector + AD vector + AE vector + AF vector ) is- (a) 2AO vector (b) 4AO vector (c) 6AO vector (d)zero

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2^i

^j + \sqrt{3}^j

A B

B C

A B C D E F

¯ ¯¯¯¯¯¯¯ ¯ C D, ¯ ¯¯¯¯¯¯¯ ¯ D E, ¯ ¯¯¯¯¯¯ ¯ F A, ¯ ¯¯¯¯¯¯ ¯ A C, ¯ ¯¯¯¯¯¯¯ ¯ A D, ¯ ¯¯¯¯¯¯ ¯ A E, ¯ ¯¯¯¯¯¯ ¯ C E

¯ ¯¯¯¯¯¯ ¯ A B + ¯ ¯¯¯¯¯¯ ¯ A C + ¯ ¯¯¯¯¯¯¯ ¯ A D + ¯ ¯¯¯¯¯¯ ¯ A E + ¯ ¯¯¯¯¯¯ ¯ A F = 3 ¯ ¯¯¯¯¯¯¯ ¯ A D = 6 ¯ ¯¯¯¯¯¯ ¯ A O

If A vector = Axi, B vector = Byj, C vector = A vector + B vector and D vector = A vector × B vector, then C vector • D vector is equal to what

A B C D E F

¯ ¯¯¯¯¯¯ ¯ A B + ¯ ¯¯¯¯¯¯ ¯ A C + ¯ ¯¯¯¯¯¯¯ ¯ A D + ¯ ¯¯¯¯¯¯ ¯ A E + ¯ ¯¯¯¯¯¯ ¯ A F = 6 ¯ ¯¯¯¯¯¯ ¯ A O

O

\vec{a}, \vec{b}

\vec{a} + \vec{b}

\vec{a} - \vec{b}

\vec{b} - \vec{a}

- (\vec{a} + \vec{b})

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