In plane vectors, we usually use ordered number pairs to represent vectors, so we can write two vectors in coordinate form. For example, the sum of vectors can be written as sum, where sum is the component of two vectors.
For the sum of two vectors, we can add their corresponding components to get a new vector, where. This new vector is the sum of vector sums, which is written as.
Geometrically, we can use directed line segments to represent vector sums, and then connect them end to end to get a parallelogram. The diagonal of this parallelogram is the sum of vector sums.
Vector addition satisfies commutative law and associative law, that is, a+b=b+a and (a+b)+c=a+(b+c). At the same time, the addition of vectors also satisfies the zero law and the anti-law, that is, a+0=a and a+(-a)=0.
Vector addition is a basic mathematical operation, which is widely used in physics, engineering, economy and other fields. For example, in physics, velocity and acceleration are both vectors, which can be synthesized by addition. In economics, the influence of multiple factors on the results can be calculated by adding vectors.
Matters needing attention in vector addition:
1, two vectors must start from * * * to be added.
2. The result of addition operation is a new vector, and its endpoint is the intersection of diagonal lines formed by line segments corresponding to the endpoints of two vectors.
3. The addition operation satisfies the commutative law and associative law, that is, a+b=b+a and (a+b)+c=a+(b+c).
4. The addition of vectors does not satisfy the law of elimination, that is, the addition of two vectors does not get a zero vector.
5. When the starting points of two vectors are the same, the parallelogram rule can be used for addition; When two vectors are connected end to end, the triangle rule can be used for addition.
6. The addition of vectors can be extended to the addition of multiple vectors, but the end-to-end connection must be guaranteed.