माना ABCDEF एक नियमित षट्भुज है। यदि \(\rm \vec{AD}=m \vec {BC}\ और\ \vec {CF}=n\vec {AB}\) है, तो mn का मान क्या है?

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

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Option 1 : -1
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गणना:

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\( \vec{AB} = 2\vec{FC} \)

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

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

इसके अलावा,

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

अब,

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

∴ mn का अंतिम मान -1 है।

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