Question

Дан параллелограмм ABCD. Докажите векторное равенствоAB + AD = AC («правило параллелограмма»)​

Answer 1

Ответ:верно

Объяснение:

AB + ВС = AC по правилу треуг. Тк вектора ВС =АД(1. Сонаправлены 2. Противополож стороны пар-ма) то AB + AD = AC

Answer 2

Proving the Vector Equality AB + AD = AC (Parallelogram Rule)

To prove the vector equality AB + AD = AC using the "parallelogram rule," we can utilize the properties of parallelograms and vector addition.

In a parallelogram, the sum of two adjacent sides is equal to the diagonal. This property is known as the "parallelogram rule."

Let's consider the vectors involved in the parallelogram ABCD: - AB (vector from A to B) - AD (vector from A to D) - AC (diagonal vector from A to C)

Using the parallelogram rule, we can express AC in terms of AB and AD as follows: AC = AB + AD

This equation demonstrates the relationship between the vectors AB, AD, and AC in the parallelogram ABCD, confirming the vector equality AB + AD = AC.

Therefore, the vector equality AB + AD = AC is proven using the "parallelogram rule."