Question

Модуль вектора а=2, модуль вектора в=4 , угол между ними=120 градусов. Найти модуль 2а-в вектора.

Answer 1

Ответ:

решение на фотографии

Answer 2

Given Information:

We are given that the magnitude of vector a is 2, the magnitude of vector b is 4, and the angle between them is 120 degrees.

Calculating the Resultant Vector:

To find the magnitude of the vector 2a - b, we can use the formula:

|2a - b| = sqrt((2a)^2 + b^2 - 2(2a)(b)cosθ)

where θ is the angle between vectors 2a and b.

Let's calculate the magnitude of the vector 2a - b using the given information.

1. First, let's calculate the magnitude of 2a: - The magnitude of 2a is given by 2 times the magnitude of a. - Since the magnitude of a is 2, the magnitude of 2a is 2 * 2 = 4.

2. Now, let's calculate the magnitude of 2a - b: - Using the formula mentioned above, we have: |2a - b| = sqrt((4)^2 + (4)^2 - 2(4)(4)cos120°)

3. Simplifying the equation: - |2a - b| = sqrt(16 + 16 - 32cos120°) - |2a - b| = sqrt(32 - 32cos120°)

4. Evaluating the cosine of 120 degrees: - The cosine of 120 degrees is -0.5.

5. Substituting the value of cos120° into the equation: - |2a - b| = sqrt(32 - 32(-0.5)) - |2a - b| = sqrt(32 + 16) - |2a - b| = sqrt(48) - |2a - b| = 4√3

Answer:

The magnitude of the vector 2a - b is 4√3.

Explanation:

The magnitude of a vector represents its length or size. In this case, we were given the magnitudes of vectors a and b and the angle between them. By using the formula for the magnitude of the resultant vector, we calculated that the magnitude of the vector 2a - b is 4√3.