Polar coordinates are used to represent how vectors are added

Knowing a=(x1,y1),b=(x2,y2), then a+b=(x1i+y1j)+(x2i+y2j)=(x1+x2)i+(y1+y2)j, i.e. a+b=(x1+x2,y1+y2). The same gives a-b=(x1-x2,y1-y2). That is, the coordinates of the sum and difference of the two vectors are equal to the sum and difference of the coordinates of the corresponding coordinates of the two vectors, respectively.

Introduction to Polar Coordinates:

Polar coordinates, which belong to the two-dimensional coordinate system, were founded by Newton.

It is mainly used in the field of mathematics. Polar coordinates refer to taking a fixed point o in the plane, called the pole, and introducing a ray ox, called the polar axis.

Select another unit of length.

and the positive direction of the angle (usually taken counterclockwise).

For any point m in the plane, the length of the line segment om is denoted by (sometimes also denoted by r), the angle from ox to om is denoted by , which is called the polar diameter of point m, which is called the polar angle of point m, and the ordinal number pair ( is called the polar coordinate of point m, and the coordinate system established in this way is called the polar coordinate system.

Typically, the polar diameter coordinate unit of m is 1 (length unit) and the polar angle coordinate unit is rad (or °).

Vector operations on polar coordinates.

The question is as follows: (p is the length, a is the angle.) If the mobile phone can't be standardized, it will be replaced) The coordinates of point A in the polar coordinates are (P, A) vector ob=2oa. So what is the polar coordinate of b?

My problem is that it doesn't conform to the vector algorithm rule. If it does, then the algorithm of whether the angle of b is a vector or not 2a is irrelevant to the coordinate system, but the vector has different coordinates in different coordinate systems.

That is to say, the set of coordinates in the Cartesian coordinate system does not apply to the coordinates in the polar coordinate system, so the angle of b is not a simple 2a. Then what does the coordinate system of the algorithm of the vector mentioned above mean, just draw a diagram to know: first write it in the form of coordinates and then multiply.

c(3cos 3,3sin 3)=(3 2,3 3 2)the same d=(-3 2,3 3 2)so.

The coordinate operation formula for vectors: a+b=(x+m,y+n). My file helper 15:35:00

Vectors were first applied to physics, and many physical quantities such as force, velocity, displacement, and electric field strength vector measures, magnetic induction, etc., are vectors. About 350 BC, the famous ancient Greek scholar Aristotle knew that force can be expressed as a vector, and the combination of two forces can be obtained by the famous parallelogram law. The term "vector" comes from directed line segments in mechanically analytic geometry.

The first to use directed line segments to represent vectors was the great British scientist Isaac Newton.

The coordinates of a vector represent the coordinates of the end point of the directed segment of the vector minus the coordinates of the start point. In the planar Cartesian coordinate system, the base vectors i and j on the x-axis and y-axis are taken respectively. To make a vector a, there is only one pair of real numbers (x, y) that is a=xi+yj, and this pair of real numbers (x,y) is called the coordinates of vector a.

Rules for the operation of vectors:

The nature of the quantitative product of vectors.

1)a·a=∣a∣²≥0

2)a·b=b·a

3)k(ab)=(ka)b=a(kb)

4)a·(b+c)=a·b+a·c

5)a·b=0<=>a⊥b

6)a=kb<=>a//b

7)e1·e2=|e1||e2|cos =cos hope mine helps you!

If the basis is a column vector, then let the column vector form the matrix a, then find the coordinates of vector b, using the formula a b, that is, the augmentation matrix can be used.

a|b, at the same time, the elementary row transformation is made, and the first n columns are transformed into an identity matrix.

Column n+1 is the coordinates.

If the basis is a row vector, then let the row vector form the matrix a, and then find the coordinates of vector b, using the formula ba, that is, the augmented matrix (a|b) t, at the same time, the elementary column transformation is made, the first n rows are transformed into an identity matrix, and the n+1 row is the coordinates.

In physics and engineering, geometric vectors are more commonly referred to as vectors. Many physical quantities.

They are all vector quantities, such as the displacement of an object, the force exerted on a ball as it hits a wall, and so on. The opposite is scalars.

That is, a quantity that has only a size and no direction. Some vector-related definitions are also closely related to physical concepts, such as the potential of a vector corresponding to the potential energy of the dissipation in physics.

The relationship between polar coordinates d and vector dx is as follows

d is the angle of each change of the polar diameter, this angle is very small, the nuclear shed is very small, so the corresponding change of the arc is also very small, so small that it can be regarded as a straight line, and because the arc is long.

It is equal to the radius multiplied by the angle, i.e., rd in the formula, so the area da of the change is equal to 1 2*r*rd (the length of the arc of this change is regarded as a straight line, i.e., a right-angled triangle.)

of the bottom edge). [0,1]dx [0,1] f(x,y) dy= f(x,y) dxdy The integration region is a rectangle: 0 x 1,0 y 1 is made as y=x The moment disruption is divided into two parts, and x=1 corresponds to the polar coordinate equation.

is: rcos = 1, that is, r = 1 cos y=1 corresponds to the polar equation is: rsin = 1, that is, r = 1 sin primitive = f(rcos, rsin) r drd = 0 4] d [0 1 cos ] f(rcos, rsin) r dr+ 4 2] d [0 1 sin ] f(rcos, rsin ) r dr

Two vectors perpendicular (such as vector a and vector b) can be obtained: multiply the two vectors to obtain 0 (i.e., a*b=0) Let the vector a=(x1,y1) and vector b=(x2,y2) be expressed by the coordinates as: a*b=x1*x2+y1*y2=0.

In the Cartesian coordinate system, take the two unit vectors i and j that are the same as the direction of the x-axis and y-axis respectively as the base, and make any vector a, which is known by the fundamental theorem of plane vectors, there is only one pair of real numbers x and y, so that a=xi+yj, and (x,y) is called the (rectangular) coordinates of vector a, which is denoted as a=(x,y). where x is called a's coordinate on the x-axis, y is called a's coordinate on the y-axis, and the above equation is called the coordinate representation of the vector.

Let the vector be the basis of r.

Let r=x1a1+..xnan

N n-element linear equations are obtained by expressing the original coordinates.

Solution (x1,..xn) is the coordinates under this set of bases.

Or: Pending coefficient method.

Let e1 and e2 be the basis vectors, and establish a system of equations about p and q on both sides of the vector m=pe1+qe2, and solve the system of equations to find p and q, for example: e1=(1,2),e2=(-2,1),m=(3,3) let (3,3)=p(1,2)+q(-2,1)=(p-2q,2p+q) so p-2q=3 and 2p+q=3, and solve p,q.

Find the coordinates of the vector under the base, if the basis is a column vector, then let the column vector form the matrix a, then find the coordinates of vector b, using the formula a b, that is, you can use the augmentation matrix a|b, at the same time, the primary row transformation, the first n columns are buried as the identity matrix, and the n+1 column is the coordinates.

If the basis is a row vector, then let the row vector form the matrix a, and then find the coordinates of vector b, using the formula ba, that is, the augmented matrix (a|b) t, at the same time, the elementary column transformation is made, the first n rows are transformed into the identity matrix, and the n+1 row is the or envy coordinates.

In physics and engineering, geometric vectors are more commonly referred to as vectors. Many physical quantities are vectors, such as the displacement of an object, the force exerted on a ball as it hits a wall, and so on. The opposite is a scalar quantity, which is a quantity that has only a magnitude and no direction.

Some vector-related definitions are also closely related to physical concepts, such as the potential of a vector corresponding to the potential energy of a frog in physics.