§ 3 number multiplication Vector

§ 3 number multiplication Vector

 

Definition 1Set to a quantity. The product of the vector and the product is a vector. Remember, the modulus is equal to the times. The direction is as follows: At that time, the direction of the vector is the same; at that time, the vector is a zero vector. At that time, the vector direction was the opposite.

In particular, the modulo of the vector is equal to the modulo of the vector, and the opposite direction is known by the definition of the negative vector :.

According to the definition of the product of vector and quantity, the number multiplication vector operation can be imported to conform to the following calculation rules:

Theorem 2.The multiplication of quantity and vector satisfies the following calculation law:

1. Combination Law, (1.3-1)

2. Allocation Law

, (1.3-2)

. (1.3-3)

Certificate1. Obviously, the vector and direction are consistent,

And

===.

2. Distribution Law 1-11

 

 

 

 

 

A common conclusion:

Theorem 3. If (number), the vector and the vector are parallel and recorded. If the vector and the vector are parallel, the vector (number) is ).

In short,.

A non-zero vector is used to represent the unit vector in the same direction.

Because it is in the same direction, it is in the same direction, and

,

That is.

We stipulate that: if.

This indicates that the modulo dividing a non-zero vector is a unit vector in the same direction as the original vector.

Note: Division operations are not defined between vectors, so formulas cannot be rewritten into forms.

Obviously, this error is caused by the "inertia" of the real number algorithm.

Example 1SetAMYes triangleABCThe midline of, verify

.

Certificate1-12,

Because,

So

However

Therefore,

That is.