Let ABCDEF be a regular hexagon. If \(\rm \vec{AD}=m \vec {BC}\ and\ \vec {CF}=n\vec {AB}\) then what is mn equal to 

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  1. -1
  2. -2
  3. 2
  4. 4

Answer (Detailed Solution Below)

Option 1 : -1
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\( \vec{AB} = 2\vec{FC} \)

\( \vec{AB} = -2\vec{CF} \)

\( n = -\frac{1}{2} \)

Also,

\( \vec{AD} = 2\vec{BC} \Rightarrow m = 2 \)

Now,

\( mn = 2 \left( -\frac{1}{2} \right) = -1 \)

∴ The final value of  is -1.

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