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TS EAMCET · Maths · Vector Algebra

If \(D, E\) and \(F\) are respectively the mid-points of \(A B, A C\) and \(B C\) in \(\triangle A B C\), then \(\overrightarrow{\mathbf{B E}}+\overrightarrow{\mathbf{A F}}\) is equal to :

  1. A \(\overrightarrow{\mathbf{D C}}\)
  2. B \(\frac{1}{2} \overrightarrow{\mathbf{B F}}\)
  3. C \(2 \overrightarrow{\mathbf{B F}}\)
  4. D \(\frac{3}{2} \overrightarrow{\mathbf{B F}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\overrightarrow{\mathbf{D C}}\)

Step-by-step Solution

Detailed explanation

Let \(A=\overrightarrow{\mathbf{a}}, B=\overrightarrow{\mathbf{b}}, C=\overrightarrow{\mathbf{c}}\) Now, \(\quad \overrightarrow{\mathbf{A F}}=\frac{1}{2}(\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}})-\overrightarrow{\mathbf{a}}\)…