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§1. 向量概念 帶有方向的量——向量——是現实世界中常見的量。它不僅是在很多數学領域里都会碰到的數学概念,而且也是在力学、物理学等科学部門中常常会接觸到的重要概念——例如力、速度等等的抽象,举例說,在力学中講到力时,不僅要考慮它的大小,而且要考慮它的作用方向,一个立方木塊放在桌子上,当我們以同样大小的力作用於这木塊上時,由於作用方向的不同,就会產生不同的結果,当力以鉛垂方向作用時,木塊保持原位不動,而当力以水平方向作用時,木塊就將向力所指的方向移動,又例如在物理学中講到位移時,同样也需要同時考慮到大小和方向,一隻輪船向东行駛10里和向南行駛10里,从其最後所处方位的來說顯然是不同的,而从輪船向东行駛10里又向南行駛10里
§1. The Vector Concept The quantity with direction — the vector — is a common quantity in the real world. It is not only a mathematical concept encountered in many fields of mathematics, but also an important concept often encountered in scientific departments such as mechanics and physics—such as the abstraction of force, speed, and so on. For example, When we talk about force in mechanics, we must not only consider its size, but also consider its direction of action. A cubic wooden block is placed on the table. When we apply the force of the same size to this block, Differently, different results will be produced. When the force acts in the vertical direction, the wood remains in place, but when the force acts in the horizontal direction, the wood moves in the direction of the force, for example in physics. When we talk about displacement, we also need to consider both the size and the direction. A ship travels 10 miles to the east and 10 miles to the south. From the perspective of its final position, it is obviously different. 10 miles east and 10 miles south