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AP EAMCET · Maths · Vector Algebra

In a regular hexagon \(A B C D E F, \overrightarrow{A B}=\vec{a}\) and \(\overrightarrow{B C}=\vec{b}\), then \(\overrightarrow{F A}=\)

  1. A \(\vec{a}-\vec{b}\)
  2. B \(\vec{a}+\vec{b}\)
  3. C \(\vec{b} \quad \vec{a}\)
  4. D \(2 \vec{b}-\vec{a}\)
Verified Solution

Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

Since, \(\overrightarrow{\mathrm{AC}}=\vec{a}+\vec{b}\) Now, \(\overrightarrow{\mathrm{FA}}+\overrightarrow{\mathrm{AC}}=\overrightarrow{\mathrm{FC}}\) \(\overrightarrow{\mathrm{FA}}+\vec{a}+\vec{b}=2 \vec{a} \Rightarrow \overrightarrow{\mathrm{FA}}=\vec{a}-\vec{b}\)