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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Vector Algebra

NDA 2024 · Mathematics · Vector Algebra

Let ABCDEF be a regular hexagon. If AD =m BC and CF =n AB , then...

Let ABCDEF be a regular hexagon. If AD→=mBC→\overrightarrow{\mathrm{AD}}=m \overrightarrow{\mathrm{BC}} and CF→=nAB→\overrightarrow{\mathrm{CF}}=n \overrightarrow{\mathrm{AB}}, then what is mnm n equal to?

Options

  1. A−4-4
  2. B−2-2
  3. C22
  4. D44

Correct answer

A. −4-4

Step-by-step solution


In a regular hexagon, AB→=2FC→⇒AB→=−2CF→∴n=−2\begin{aligned} & \overrightarrow{\mathrm{AB}}=2 \overrightarrow{\mathrm{FC}} \\ & \Rightarrow \overrightarrow{\mathrm{AB}}=-2 \overrightarrow{\mathrm{CF}} \\ & \therefore \mathrm{n}=-2 \end{aligned} Also, AD→=2BC→∴m=2\overrightarrow{\mathrm{AD}}=2 \overrightarrow{\mathrm{BC}}\therefore \quad \mathrm{m}=2 Now, mn=2(−2)=−4m n=2(-2)=-4
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