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AP EAMCET · Maths · Straight Lines

If \(\mathrm{L}, \mathrm{M}, \mathrm{N}\) are the mid points of the sides \(\mathrm{PQ}, \mathrm{QR}\) and RP of \(\triangle \mathrm{PQR}\) respectively. then
\(\overrightarrow{Q M}+\overrightarrow{L N}+\overrightarrow{M L}+\overrightarrow{R N}-\overrightarrow{M N}-\overrightarrow{Q L}=\)

  1. A \(\overrightarrow{P Q}+\overrightarrow{Q R}+\overrightarrow{L M}+\overrightarrow{M N}\)
  2. B \(\overrightarrow{L P}+\overrightarrow{P M}+\overrightarrow{M Q}\)
  3. C \(\overrightarrow{P Q}+\overrightarrow{Q R}-\overrightarrow{P R}\)
  4. D \(\overrightarrow{L M}+\overrightarrow{M N}+\overrightarrow{N R}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\overrightarrow{P Q}+\overrightarrow{Q R}-\overrightarrow{P R}\)

Step-by-step Solution

Detailed explanation

In \(\triangle P Q R, M\) and \(N\) are mid-points of \(\overrightarrow{Q R}\) and \(\overrightarrow{R P}\) So, \(\overrightarrow{M N}=\frac{1}{2} \overrightarrow{P Q} \Rightarrow \overrightarrow{M N}=\overrightarrow{L P}=\overrightarrow{L Q}\) So,…