对于具有大小和方向的量的矢量的加和减，有特殊的程序。可以使用图形方法或向量组件来添加和减去向量。本文解释了这两种方法。首先，让我们看看如何以图形方式添加向量。

如何以图形方式添加向量

Suppose we need to add the two vectors,   and  . 

Graphically, we place the “tail” of one of the vectors on the “nose” of the other vector. The resultant vector, i.e. the vector   , is the vector that goes from the tail of the first vector to the nose of the last vector. Note that we can repeat this procedure to add any number of vectors. In practice, to do this, one may need to make a scale diagram of the vectors on a paper.

Vector addition is commutative, i. e.  . Graphically, we can show this by starting with  and then adding  to it. Since the resultant vector in both cases have the same size and direction, the resultant vectors are equal. This shows that the order in which vectors are added does not matter.

Also, vector addition is associative, i.e.  . This means that the order in which vectors are grouped during addition does not matter.

如何使用组件添加向量

Suppose the vector  and the vector . Then, the vector .

例子

Two forces and  act on a body. The forces are given by the vectors  and  . Find the resultant force  .

.

同样地，减去向量也需要将向量的负数相加。

向量的负数

For a given vector  , the negative vector  has the same magnitude as  but points in the opposite direction.

如何以图形方式减去向量

Subtracting a vector is equivalent to adding the negative vector. i.e.  . Graphically, we can show this as follows:

We need to subtract  from  .

We identify the negative vector of  . Then,  :

如何使用分量减去向量

Suppose the vector  and the vector . Then, the vector .

例如，可以通过减去两个位置向量来找到粒子的位移。例如，见关于置换的文章。

如何乘向量