Question

A(1;-2;2) b(-4;3;0) найдите косинус угла

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To find the cosine of the angle between two vectors, you can use the dot product formula. Let's denote vector A as A(a1, a2, a3) and vector B as B(b1, b2, b3). The dot product of two vectors A and B is given by:

A · B = (a1 * b1) + (a2 * b2) + (a3 * b3)

The magnitude (length) of a vector A is given by:

|A| = √(a1^2 + a2^2 + a3^2)

The cosine of the angle θ between the two vectors A and B can be calculated as follows:

cos(θ) = (A · B) / (|A| * |B|)

Let's calculate the cosine of the angle between vectors A and B:

Vector A: (1, -2, 2) Vector B: (-4, 3, 0)

Dot product of A and B: A · B = (1 * -4) + (-2 * 3) + (2 * 0) = -4 - 6 + 0 = -10

Magnitude of vector A: |A| = √(1^2 + (-2)^2 + 2^2) = √(1 + 4 + 4) = √9 = 3

Magnitude of vector B: |B| = √((-4)^2 + 3^2 + 0^2) = √(16 + 9 + 0) = √25 = 5

Now, plug the values into the cosine formula:

cos(θ) = (A · B) / (|A| * |B|) = -10 / (3 * 5) = -10 / 15 = -2/3

So, the cosine of the angle between vectors A and B is -2/3.