Question

Диагонали параллелограмма ABCD пересекаются в точке O. Выразите векторы ad и vector dc через векторы vector oc = a и vector bo = b. Выполните рисунок к заданию.

Answer 1

Ответ: см. во вложении

Объяснение: там же

Answer 2

Ответ:

Применяем правило треугольника сложения векторов . Смотри рисунок

$\overline{DC}=\overline{AB}=\overline{AO}+\overline{OB}=\overline{OC}-\overline{BO}=\vec{a}-\vec{b}\\\\\\\overline{AD}=\overline{AO}+\overline{OD}=\overline{OC}+\overline{BO}=\vec{a}+\vec{b}$  

Answer 3

Parallelogram ABCD and its Diagonals

In a parallelogram ABCD, the diagonals intersect at point O. We are asked to express vectors AD and DC in terms of vectors OC = A and BO = B.

To find vector AD, we can use the fact that in a parallelogram, opposite sides are parallel and equal in length. Therefore, vector AD is equal to vector OC plus vector BO.

AD = OC + BO.

Similarly, to find vector DC, we can use the fact that in a parallelogram, opposite sides are parallel and equal in length. Therefore, vector DC is equal to vector BO minus vector OC.

DC = BO - OC.

Let's illustrate this with a diagram:

     A _______ B
      |       |
      |       |
      |       |
      |_______|
     D         C

In this diagram, O represents the point of intersection of the diagonals AC and BD. Vector OC represents the vector from O to C, and vector BO represents the vector from B to O.

Using the expressions we derived earlier, we can find vector AD and vector DC.

I hope this helps! Let me know if you have any further questions.