 רҵ����
��ϵ��ʽ
���Ǵ�����ѵѧУ

��ַ�����������������ʹ��10606�ţ�ɽ������ѧԺ������500��·�ϣ�
�绰��400-9922-676
QQ��800-11-7777
�� �䣺3323909298@qq.com

�����ڵ�λ�ã���ҳ > ������Ϣ > ������Ϣ
�߿���ѧƽ��������ʽ������Щ��һ����
���ߣ�admin �����ڣ�2019-08-06 15:11 �������

ƽ���������ڶ�άƽ���ڼ��з���(direction)���д�С(magnitude)����������ѧ��Ҳ����ʸ������֮��Ե���ֻ�д�С��û�з������������������ƽ��������a,b,c�����һ��С��ͷ��ʾ��Ҳ�����ñ�ʾ�����������߶ε������յ���ĸ��ʾ������������������ƽ�������Ĺ�ʽ

��ѧ3 (2).jpg

1�������ļӷ�

�����ļӷ�����ƽ���ı��η���������η���
AB+BC=AC��
a+b=(x+x'��y+y')��
a+0=0+a=a��
�����ӷ��������ɣ�
�����ɣ�a+b=b+a��
����ɣ�(a+b)+c=a+(b+c)��
2�������ļ���
���a��b�ǻ�Ϊ�෴����������ôa=-b��b=-a��a+b=0. 0�ķ�����Ϊ0
AB-AC=CB. ��“��ͬ��㣬ָ�򱻼�”
a=(x,y) b=(x',y') �� a-b=(x-x',y-y').
3����������
ʵ��λ������a�ĳ˻���һ������������λa���ҨOλa�O=�Oλ�O?�Oa�O��
��λ��0ʱ��λa��aͬ����
��λ��0ʱ��λa��a������
��λ=0ʱ��λa=0���������⡣
��a=0ʱ����������ʵ��λ������λa=0��
ע��������֪�����λa=0����ôλ=0��a=0��
ʵ��λ��������a��ϵ������������λa�ļ���������ǽ���ʾ����a�������߶��쳤��ѹ����
���Oλ�O��1ʱ����ʾ����a�������߶���ԭ����λ��0���򷴷���λ��0�����쳤Ϊԭ���ĨOλ�O����
���Oλ�O��1ʱ����ʾ����a�������߶���ԭ����λ��0���򷴷���λ��0��������Ϊԭ���ĨOλ�O����
���������ĳ˷����������������
����ɣ�(λa)?b=λ(a?b)=(a?λb)��
�����������ķ����ɣ���һ�����ɣ���(λ+μ)a=λa+μa.
�����������ķ����ɣ��ڶ������ɣ���λ(a+b)=λa+λb.
������������ȥ�ɣ��� ���ʵ��λ≠0��λa=λb����ôa=b���� ���a≠0��λa=μa����ôλ=μ��
4�������ĵ�������
���壺��֪������������a,b.��OA=a,OB=b,���AOB��������a������b�ļн�,������a,b�����涨0≤��a,b��≤π
���壺�������������������ڻ����������һ������,����a?b.��a��b������,��a?b=|a|?|b|?cos��a,b������a��b����,��a?b=+-�Oa�O�Ob�O.
�������������������ʾ��a?b=x?x'+y?y'.
��������������������
a?b=b?a�������ɣ���
(λa)?b=λ(a?b)(�������˷��Ľ����)��
��a+b)?c=a?c+b?c�������ɣ���
������������������
a?a=|a|��ƽ��.
a⊥b ��=��a?b=0.
|a?b|≤|a|?|b|.
��������������ʵ���������Ҫ��ͬ��
1������������������������,����(a?b)?c≠a?(b?c)�����磺(a?b)^2≠a^2?b^2.
2����������������������ȥ��,������ a?b=a?c (a≠0),�Ʋ��� b=c.
3��|a?b|≠|a|?|b|
4���� |a|=|b| ,�Ʋ��� a=b��a=-b.

Planar vectors are quantities of both direction and magnitude in two-dimensional planes. They are also called vectors in physics, as opposed to quantities of only size and no direction. Planar vectors are represented by a small arrow on a, B and c, or by the beginning and end letters of the directed line segments representing vectors. Here are the formulas of the plane vectors sorted out.

Mathematics 3(2). jpg

The addition of vectors satisfies the parallelogram rule and the triangle rule.
AB + BC = AC.
A + b= (x + x', y + y').
A + 0 = 0 + a = a.
Operational Law of Vector Addition:
Exchange law: a + B = B + a;
The law of association: (a + b) + C = a + (b + c).
2. Subtraction of Vectors
If A and B are opposite vectors, then the reverse of a=-b, b=-a, a+b=0.0 is 0.
AB-AC = CB. That is "common starting point, pointing to be subtracted"
A= (x, y) b= (x', y') then a-b= (x-x', y-y').
3. Multiplier Vector
The product of real number lambda and vector a is a vector, which is denoted as lambda, and lambda=lambda_a.
When lambda > 0, lambda A and a are in the same direction.
When lambda is less than 0, lambda A and a are in the opposite direction.
When lambda = 0, lambda = 0, any direction.
When a = 0, for any real number lambda, there is lambda = 0.
Note: By definition, if lambda = 0, then lambda = 0 or a = 0.
Real number lambda is called the coefficient of vector a. The geometric meaning of multiplier vector lambda is to extend or compress the directed line segment representing vector a.
When lambda > 1, the directed line segment representing vector a extends to lambda times the original direction (lambda > 0) or the opposite direction (lambda < 0).
When lambda < 1, the directed line segment representing vector a is shortened to lambda times the original direction (lambda > 0) or the opposite direction (lambda < 0).
The multiplication of numbers and vectors satisfies the following operation laws
The law of association: (lambda) B = lambda (a b) = (a lambda b).
Distribution Law of Vector to Number (First Distribution Law): (lambda+mu) a = lambda+mua.
The law of distribution of numbers to vectors (the second law of distribution): lambda(a+b)=lambda+lambda.
Elimination law of multiplier vectors: 1. If real number lambda 0 and lambda = lambda b, then a = B. (2) If a_0 and lambda = mua, then lambda = mu.
4. Quantitative Product of Vectors
Definition: If two non-zero vectors a, B. are known as OA = A and OB = b, then the angle AOB is called the angle between vector a and vector b, which is recorded as a, B and stipulates that 0 a, B is less than pi.
Definition: The quantity product of two vectors (inner product and dot product) is a quantity, which is denoted as a B. If A and B are not collinear, then a b= | B cos a, B and if a and B are collinear, then a b=+ - a B.
The coordinates of the quantity product of vectors are expressed as a B = x x'+y y'.
Operational Law of Quantity Product of Vectors
A * b = b * a (exchange law);
(lambda) B = lambda (a b) (on the law of combination of number multiplication);
(a + b) * C = a * C + b * C (distribution law);
The Properties of the Quantity Product of Vectors
A * a= | a | squared.
A B = a B = 0.
| a * B | < | a | | B |.
The Main Differences between the Quantitative Product of Vectors and Real Number Operations
1. The number product of vectors does not satisfy the binding law, i.e. (a b) C a (b c); for example, (a b) 2 a 2 B 2.
2. The number product of vectors does not satisfy the elimination law, that is, from a B = a C (a 0), B = C can not be deduced.
3. |a.b | | a | | b|
4. From | a |= | B |, we can not deduce a = B or a= - B.

��һƪ����һ����δ������һ��������

���߿ͷ�

������ѯ  ������ѯ  ֣�������� ���Ǵ���ѧУ ѧУ����ȫְ��ְԱ��100���ˣ����о����м�����ְ�Ƶ�Լ50%����˶ʿѧλ��Լ30%����λ��ʦ������ؼ���ʦ���Ͷ�ģ���ͽ�ѧ���֡�ѧ�ƴ�ͷ�ˡ����㵳Ա����������ε������ƺţ�ѧУ��ʦ������ʦ�º͸�ˮƽ�Ľ�����ѧ��������֤��ѧУ�Ľ����ͽ�ѧ�������ܵ�ѧ���ͼҳ���һ�º����� ���ϴ����߿���ѵѧУ ���ϴ����߿������� ���ϴ����߿���ѵ��