Question

ДАЮ 40 БАЛІВ Чи всі вектори, які колінеарні нуль-вектору, колінеарні між собою?

Answer 1

нет. любой вектор коллинеарен нулевому вектору, но между собой они могут быть и неколлинеарны.

Answer 2

Understanding Vector Collinearity

When considering whether all vectors that are collinear to the zero vector are collinear to each other, it's important to understand the concept of collinearity in the context of vectors.

Collinearity refers to the property of lying on the same straight line or being parallel to each other. In the context of vectors, collinear vectors are those that are scalar multiples of each other, meaning one can be obtained from the other by scaling.

Relationship Between Vectors and the Zero Vector

In the context of vectors, the zero vector is a special vector with a magnitude of zero. It is denoted as 0 and has no specific direction. Any vector that is a scalar multiple of the zero vector is also the zero vector. This means that all vectors collinear to the zero vector are, in fact, the zero vector itself.

Collinearity of Vectors Collinear to the Zero Vector

Given that all vectors collinear to the zero vector are, in fact, the zero vector, it follows that they are collinear to each other. This is because any non-zero vector is a scalar multiple of the zero vector, and since scalar multiplication preserves collinearity, all non-zero vectors collinear to the zero vector are collinear to each other.

In summary, all vectors that are collinear to the zero vector are indeed collinear to each other due to the nature of scalar multiplication and the properties of the zero vector.

I hope this explanation helps clarify the concept of collinearity in the context of vectors! If you have any more questions or need further clarification, feel free to ask.