벡터의 뜻, 용어와 기호
벡터의 뜻
우리가 사용하는 양 가운데에서 길이, 넓이, 부피, 속력 등은 크기만을 가지고 있으므로 그 양을 하나의 실수로 나타낼 수 있다. 하지만 속도, 가속도, 힘 등은 크기와 함께 방향도 생각해야 그 양을 나타낼 수 있다.
일반적으로 크기만을 가지는 양을 스칼라(scalar)라고 하고, 크기와 방향을 함께 가지는 양을 벡터(vector)라 한다. 특히 평면에서의 벡터를 평면벡터라 한다.
벡터의 용어와 기호
벡터를 그림으로 나타낼 때는 아래 그림과 같이 방향이 주어진 선분을 이용한다. 점 에서 점 로 향하는 주어진 선분 를 벡터 라 하며, 기호로
와 같이 나타낸다.
이때 점 를 벡터 의 시점, 점 를 벡터 의 종점이라 한다.
벡터를 한 문자로 나타낼 때는 기호로
와 같이 나타낸다.
벡터의 크기
또 선분 의 길이를 벡터의 크기라 하며, 기호로
또는
와 같이 나타낸다. 특히 크기가 인 벡터를 단위벡터라 한다.
![](data:image/png;base64,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)
영벡터
한편 벡터 와 같이 시점과 종점이 일치하는 벡터를 영벡터라고 하며 기호로 와 같이 나타낸다. 영벡터의 크기는 이고 그 방향은 생각하지 않는다.