Question

сторона квадрата АВСД = 12. Найдите скалярное произведение векторов АВ и ВД.Помогите пожалуйста, очень срочно)))

Answer 1

1) AB * BD = AB * BD * cos(AB^BD)

2) Найдем BD  по теореме пифагора:

AB^2+AD^2 = BD^2

12^2 + 12^2 = x^2

144+144 = 288, BD = sqrt288

3) cos 45 = 1/sqrt2

4) 12*sqrt288*1/sqrt2 = 12*sqrt144 = 12*12 = 144

ответ: 144

P.S sqrt - обозначение корня

Answer 2

Finding the Side Length of Square ABCD

To find the scalar product of vectors AB and AD, we first need to determine the side length of square ABCD. The side length of a square can be found using the formula:

Side Length of Square ABCD = 12

Calculating the Scalar Product of Vectors AB and AD

The scalar product (also known as the dot product) of two vectors is calculated using the formula: A · B = |A| |B| cos(θ), where |A| and |B| are the magnitudes of the vectors, and θ is the angle between them.

Given that AB and AD are two sides of the square, they are perpendicular to each other, and the angle between them is 90 degrees. Therefore, the cosine of 90 degrees is 0, and the scalar product simplifies to:

AB · AD = |AB| * |AD| * cos(90°) = |AB| * |AD| * 0 = 0

So, the scalar product of vectors AB and AD is 0.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.