MHT CET · Maths · Vector Algebra
\(M\) and \(N\) are the mid points of the diagonals \(A C\) and \(B D\) respectively of quadrilateral \(A B C D,\) then
\(\overrightarrow{A B}+\overrightarrow{A D}+\overrightarrow{C B}+\overrightarrow{C D}=\)
- A
- B
- C
- D
Answer & Solution
Correct Answer
(C)
Step-by-step Solution
Detailed explanation
\(\overline{A B}+\overline{A D}+\overline{C B}+\overline{C D}=\ldots\)
\(=(\bar{b}-\bar{a})+(\bar{d}-\bar{a})+(\bar{b}-\bar{c})+(\bar{d}-\bar{c})\)
\(=2[(\bar{b}+\bar{d})-(\bar{a}+\bar{c})]=4\left[\left(\frac{\bar{b}+\bar{d}}{2}\right)-\left(\frac{\bar{a}+\bar{c}}{2}\right)\right]=\) \(4 \bar{M} N\)
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