Вежби од точка,права,рамнина и две прави

1. Правите a и b не се сечат. Тогаш тие може да не лежат во иста рамнина?

True

False

If the lines a and b do not intersect, it means that they do not cross each other or share a common point. In this case, it is possible for them to not lie in the same plane. This is because planes are infinite and can exist in three-dimensional space, while lines can be contained within a plane or extend beyond it. Therefore, the statement "they may not lie in the same plane" is true.

Explanation

If the lines a and b do not intersect, it means that they do not cross each other or share a common point. In this case, it is possible for them to not lie in the same plane. This is because planes are infinite and can exist in three-dimensional space, while lines can be contained within a plane or extend beyond it. Therefore, the statement "they may not lie in the same plane" is true.

2. Точката А лежи во рамнината .Тогаш правата што минува низ таа точка може да лежи во рамнината.

да

не

In the given statement, it is mentioned that point A lies in the plane. Therefore, any line passing through point A will also lie in the same plane. This is because a plane is a two-dimensional surface that extends infinitely in all directions, and any line passing through a point in that plane will also lie within that plane. Hence, the answer is "да" (yes).

Explanation

In the given statement, it is mentioned that point A lies in the plane. Therefore, any line passing through point A will also lie in the same plane. This is because a plane is a two-dimensional surface that extends infinitely in all directions, and any line passing through a point in that plane will also lie within that plane. Hence, the answer is "да" (yes).

3. За кои четири точки се веки дека се компланарни?

точките од кои две по две лежат на две рамнини

точките кои лежат на иста права

точките кои лежат во иста рамнина

точките од кои две по две лежат на две разминувачки прави

The correct answer is "точките кои лежат во иста рамнина" which translates to "the points that lie in the same plane." This means that the given points are all located in the same two-dimensional surface.

Explanation

The correct answer is "точките кои лежат во иста рамнина" which translates to "the points that lie in the same plane." This means that the given points are all located in the same two-dimensional surface.

4. Две прави да имаат само две заеднички (различни ) точки

True

False

The statement says that two lines should have only two common points, which are different from each other. This statement is false because two lines can have either no common points, one common point, or infinitely many common points. It is not necessary for two lines to have exactly two distinct common points. Therefore, the correct answer is false.

Explanation

The statement says that two lines should have only two common points, which are different from each other. This statement is false because two lines can have either no common points, one common point, or infinitely many common points. It is not necessary for two lines to have exactly two distinct common points. Therefore, the correct answer is false.

5. Колку најмногу рамнини може да се определат со точките A,B,C,D,E ако кои било четири од нив не се компланарни

8

10

12

14

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Explanation

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6. Колку најмногу рамнини минуваат низ две точки

бецконечно многу

една

две

три

not-available-via-ai

Explanation

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7. Колку најмногу прави може да се определат со точките A,B,C,D,E ако кои било три од нив не се колинеарни

4

8

10

12

If any three points are not collinear, then they can form a triangle. In a triangle, the maximum number of sides or lines that can be formed is 3. Therefore, with the given points A, B, C, D, E, the maximum number of lines that can be formed is 3. Each line is formed by connecting two points. So, the maximum number of lines or sides that can be formed is 3, which means the answer is 10.

Explanation

If any three points are not collinear, then they can form a triangle. In a triangle, the maximum number of sides or lines that can be formed is 3. Therefore, with the given points A, B, C, D, E, the maximum number of lines that can be formed is 3. Each line is formed by connecting two points. So, the maximum number of lines or sides that can be formed is 3, which means the answer is 10.

8. На цртежот е претставен квадар ABCDEFGH. Правата EF го содржи работ EF. Кои прави се сечат со EF?

AE и HE

DE и GE

CF и DF

BF и GF

The correct answer is AE и HE, BF и GF. In the given diagram, the line EF is shown passing through the points E and F. To determine which lines intersect with EF, we need to identify the lines that also pass through points A, H, B, and G. From the options given, lines AE and HE both pass through point A and intersect with EF. Similarly, lines BF and GF both pass through point B and intersect with EF. Therefore, the correct answer is AE и HE, BF и GF.

Explanation

The correct answer is AE и HE, BF и GF. In the given diagram, the line EF is shown passing through the points E and F. To determine which lines intersect with EF, we need to identify the lines that also pass through points A, H, B, and G. From the options given, lines AE and HE both pass through point A and intersect with EF. Similarly, lines BF and GF both pass through point B and intersect with EF. Therefore, the correct answer is AE и HE, BF и GF.

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9. Колку рамнини определуваат три прави кои минуваат низ иста точка

The question is asking how many planes can be determined by three lines passing through the same point. In three-dimensional space, three non-parallel lines passing through the same point will determine a unique plane. Therefore, the correct answer is 3.

Explanation

The question is asking how many planes can be determined by three lines passing through the same point. In three-dimensional space, three non-parallel lines passing through the same point will determine a unique plane. Therefore, the correct answer is 3.

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