The content of your image is written in Russian and covers concepts related to the "Mechanical Meaning of Vector Product" and the "Equation of a Line Segment in the Plane." Let's break down the questions for clarity.

1. Mechanical Meaning of the Vector Product: This section appears to explore the moment of force $\vec{F}$ applied at point $A$ relative to a point $O$. The moment is expressed in various forms, such as $M_O(\vec{F}) = [\vec{OA}, \vec{F}]$ and similar notations. Each option likely tests the understanding of the correct formulation of the vector cross-product to describe torque or moments in mechanics.

2. Equation of a Line Segment in the Plane: This question presents various forms of line equations:

   • $Ax + By + C = 0$: A general form of the line equation.
   • $y = kx + b$: The slope-intercept form of a line.
   • $\frac{x}{a} + \frac{y}{b} = 1$: The intercept form, typically used when the line intersects the x- and y-axes at $a$ and $b$, respectively.
   • $A(x - x_0) + B(y - y_0) = 0, \, (A^2 + B^2 \neq 0)$: Another form of a line equation, based on a point $(x_0, y_0)$ and a direction vector $(A, B)$.

If you need help solving these questions or interpreting the answers, feel free to ask!

Follow-Up Questions

1. What is the vector product (or cross product) and how does it relate to torque in physics?
2. How does the intercept form of a line equation help in determining where a line intersects the axes?
3. Why is the general form $Ax + By + C = 0$ often used for line equations?
4. What conditions determine when we can use $M_O(\vec{F}) = [\vec{OA}, \vec{F}]$ for moments?
5. How is the point-direction form of a line equation useful in applications?

Tip:

Understanding different forms of line equations helps you quickly identify properties like slope, intercepts, and relationships to points on the line in coordinate geometry.