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
\(\overrightarrow{Q M}+\overrightarrow{L N}+\overrightarrow{M L}+\overrightarrow{R N}-\overrightarrow{M N}-\overrightarrow{Q L}=\)
- A \(\overrightarrow{P Q}+\overrightarrow{Q R}+\overrightarrow{L M}+\overrightarrow{M N}\)
- B \(\overrightarrow{L P}+\overrightarrow{P M}+\overrightarrow{M Q}\)
- C \(\overrightarrow{P Q}+\overrightarrow{Q R}-\overrightarrow{P R}\)
- D \(\overrightarrow{L M}+\overrightarrow{M N}+\overrightarrow{N R}\)
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,…
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