Question

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

Answer 1

Ответ: во вложении

Объяснение: там же

Answer 2

Ответ:

Применяем правило треугольника сложения векторов . Смотри рисунок .

Используем также свойства параллелограмма: а) диагонали параллелограмма в точке пересечения делятся пополам : AO=OC , BO=OD ; б) противоположные стороны параллелограмма равны и параллельны: DC=AB , AD=BC .

Также надо помнить, что возможен параллельный перенос векторов на плоскости .

Векторы  называются равными, если они имеют одинаковую длину, лежат на параллельных прямых или на одной прямой, и направлены в одном направлении, поэтому  $\overline{DC}=\overline{AB}\ ,\ \ \overline{AO}=\overline{OC}\ ,$

$\overline{OD}=\overline{BO}$  .

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

Answer 3

Diagonals of Parallelogram ABCD

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 solve this problem, we can use the properties of parallelograms and vector addition.

Solution:

1. First, let's draw a diagram to visualize the given information. The diagram will show the parallelogram ABCD with the diagonals intersecting at point O.


2. Now, let's express vector AD in terms of vectors OC = A and BO = B.

According to the properties of parallelograms, the diagonals of a parallelogram bisect each other. This means that the vector OC bisects the vector AD at point O.

Therefore, we can express vector AD as the sum of vectors AO and OD:

AD = AO + OD

Since vector AO is equal to vector OC (A = OC) and vector OD is equal to vector BO (D = BO), we can substitute these values into the equation:

AD = A + B

3. Next, let's express vector DC in terms of vectors OC = A and BO = B.

According to the properties of parallelograms, the diagonals of a parallelogram bisect each other. This means that the vector BO bisects the vector DC at point O.

Therefore, we can express vector DC as the sum of vectors DO and OC:

DC = DO + OC

Since vector DO is equal to vector BO (D = BO) and vector OC is equal to vector A (O = A), we can substitute these values into the equation:

DC = B + A

Conclusion:

In summary, the vectors AD and DC can be expressed as follows:

- Vector AD = A + B - Vector DC = B + A

Please refer to the diagram for a visual representation of the parallelogram ABCD with the intersecting diagonals.

Note: The diagram provided in this response is for illustrative purposes only and may not accurately represent the specific parallelogram ABCD described in the question.