Problem S:L25.296 of Vector Calculus in Parallelogram // Parallelogrammda vektorlı esaplavnıñ 296-nci meselesi

 "Gazeta Matematika. Meşğuliyetlernen qoşma" 10/2025 sanlı mecmuasından alındı, 10 saife.

          To further practice vector calculus, consider the problem (in translation):

 "Consider the parallelogram  $ABCD$  and the points  $M\in AB,\; N \in AC$

              such that  $\overrightarrow{AM}=\frac{1}{4}\overrightarrow{AB},\;\; \overrightarrow{AN}=\frac{1}{5}\overrightarrow{AC}$. Express the vectors  $\overrightarrow{DN},\; \overrightarrow{MN}$

  in terms of the vectors  $\overrightarrow{AB}$  and $\overrightarrow{AD}$ , and then show that

                                           the points  $D,\; N,\; M$ are collinear.

 No author."

We will use formulas from the February 20, 2024 Post "Barycentric coordinate on the Straight Line".

Figure according to the statement. The green line  $k$  is a suggestion of the conclusion.

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