The formula for calculating the perpendicularity of vectors, the perpendicular formula for vectors

a, b are two vectors, a=(a1,a2)b=(b1,b2), a b:a1 b1=a2 b2 or a1b1=a2b2 or a= b, is a constant, a vertical b: a1b1+a2b2=0.

Let the two vectors be vector a and vector b, and vector a = kx vector b (k is a constant), vector a and vector b are parallel, and vector a?When vector b=0, vector a and vector b are perpendicular.

The ratio of the equal parallel product yields -1 perpendicular, the vector a=(x1,y1)b=(x2,y2), parallel: x1y2-x2y1=0. Vertical:

The slope of x1x2+y1y2= is y1 x1b and the slope of x1b is y2 x2, then according to the slope of the straight line, there are two straight lines parallel to y1 x1=y2 x2 is the formula of the vector parallel you asked, according to the slope of the straight line, there are two straight lines perpendicular to y1 x1*y2 x2=-1 is the formula of the vector perpendicular you asked.

If a=(x,y), b=(x,y) if a?b = 0 (order of magnitude a and b.)

That is, xx+yy=0, then a b. If a b = 0, then vector a is parallel to vector b; a=b, and a is also parallel to b.

The coordinates of the vector a=(x1,y1) and the vector b=(x2,y2) are met.

x1x2+y1y2=0

This formula can be simply written as: multiplying in the same direction equals 0

Vector Vertical Formula:a, b are two vectors, a=(a1,a2),b=(b1,b2)a b:a1 b1=a2 b2 or a1b1=a2b2 or a= b, is a constant.

a vertical b: a1b1 + a2b2 = 0.

Vectors were first applied to physics, and many physical quantities such as force, velocity, displacement, as well as the strength of electric fields and magnetic inductions.

and so on are vectors. About 350 BC, ancient Greece.

Famous scholar Aristotle.

Knowing that forces can be expressed as vectors, the combined action of two forces can be obtained using the famous parallelogram rule.

Vector vertical note:

1. If the direction vector of a straight line.

Parallel to the normal vector of the plane, the line is perpendicular to the plane.

2. If the direction vector of the straight line is perpendicular to the normal vector of the plane.

3. If there is no intersection between the straight line and the plane, the straight line is parallel to the plane.

4. If the straight line has an intersection point with the plane, the straight line is on the plane.

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Through this property, some unknowns can be solved, etc.

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Let the coordinates of vector a be x,y

Vector a|²＝x²＋y²＝52

Vector A Vector B, 2x 3y 0

From the solution of x6,y4 or x6,y4, so the coordinates of vector a are 6,4 or 6,4

1. Vector vertical formula.

Vector a=(a1,a2), vector b=(b1,b2)a b: a1 b1=a2 b2 or a1b1=a2b2 or a= b ( is a constant).

a vertical b: a1b1 + a2b2 = 0.

2. Vector parallel formula.

Vector a=(x1,y1), vector b=(x2,y2)x1y2-x2y1=0

a b.

is a·b = 0, i.e. (x1x2 + y1y2) = 0<>

a, b are two vectors.

a=（a1,a2），b=（b1,b2）

a b: a1 b1=a2 b2 or a1b1=a2b2 or a= b, is a constant.

a vertical b: a1b1 + a2b2 = 0.

History of vector developmentVectors were first applied to physics, and many physical quantities such as force, velocity, displacement, electric field strength, magnetic induction strength, 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.

From the perspective of the history of mathematics, for a long time in history, the vector structure of space was not recognized by mathematicians, until the end of the 19th century and the beginning of the 20th century, people related the nature of space with vector operations, so that vectors have become a set of mathematical systems with excellent generality of operations.

The calculation formula is: the sufficient and necessary condition of a b is a·b=0, that is, (x1x2+y1y2)=0.

In mathematics, a vector (also known as a Euclidean vector, geometric vector, vector), refers to a quantity with magnitude and direction. It can be visualized as a line segment with an arrow.

I am Mr. Dong Xiaoming, and I am good at mathematics, physics and chemistry.

I will provide you with the process and answer in 5 minutes, please wait.

The two vectors are perpendicular and the corresponding coordinates are multiplied and the sum is 0.

Through this property, some unknowns can be solved, etc.

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In two-dimensional space, a vector can be represented as a=(x,y) (pointing from point (0,0) to point (x,y)).

If the vector a=(x1,y1) is perpendicular to the vector b=(x2,y2), then there is x1*x2+y1*y2=0

If you don't use coordinates, the inner product of a and b = |a|*|b|*cos (the angle between a and b) = 0

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 Two vectors are parallel (such as vector a and vector b) Let the vector a=(x1,y1) and vector b=(x2,y2) get: x1y2-x2y1=0 Hope it helps!

Vector a=(x1,y1), vector b=(x2,y2).

Perpendicular coordinates satisfy.

x1x2+y1y2=0

This formula can be simply written as: multiplying in the same direction equals 0

Vector parallel: the cross-product difference is 0, i.e., x1y2-x2y1=0

Vector perpendicular: the sum of the multiplication is 0, that is, x1y1+x2y2=0

a, b are two vectors.

a=（a1,a2），b=（b1,b2）

a b: a1 b1=a2 b2 or a1b1=a2b2 or a= b, is a constant.

a vertical b: a1b1 + a2b2 = 0.

History of vector development

Vectors were first applied to physics, and many physical quantities such as force, velocity, displacement, electric field strength, magnetic induction strength, etc., are vectors. About 350 B.C., 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 nucleus shape modification law.

There are two vectors a and b, and the sufficient and necessary conditions for a b are a·b=0, i.e., (x1x2+y1y2)=0.

For the perpendicular problem in solid geometry, it mainly involves the line-plane perpendicularity problem and the surface-to-surface perpendicularity problem, and the difficulty in solving the related problems is the definition of line-plane perpendicularity and the understanding of the conditions for determining the validity of the theorem. The determination theorem of perpendicular two planes and its application and the understanding of the concept of dihedral angle.

Summary. Hello, glad to answer for you. The vector vertical formula is:

a, b are two vectors, a=(a1,a2),b=(b1,b2)a b:a1 b1=a2 b2 or a1b1=a2b2 or a= b, is a constant. A vertical B:

a1b1+a2b2=0。

Hello, glad to answer for you. The straight formula for the vector is as follows: a, b are two vectors, a=(a1,a2),b=(b1,b2)a b:

a1 b1=a2 b2 or a1b1=a2b2 or a= b, is a constant old sign. a vertical b: a1b1 + a2b2 = 0.

Extended information: Vectors were first applied to physics, and many physical quantities such as force, velocity, displacement, electric field strength, magnetic induction strength, etc. are vectors. About 350 B.C., the famous ancient Greek scholar Aristotle knew that force can be represented as a vector, and the combination of two forces can be obtained by taking the famous parallelogram law from Dong Xian.

Let a,b be two vectors, a=(a1,a2),b=(b1,b2),a b:a1 b1=a2 b2 or a1b1=a2b2 or a= b, is a constant. a vertical b: a1b1 + a2b2 = 0.

Geometric angle: vector a (x1, y1), length l1 = x1 +y1 )

Vector b (x2,y2), length l2 = x2 +y2 )

The distance from x1,y1) to (x2,y2): d= [x1 - x2) y1 - y2)].

The two vectors are perpendicular, according to the Pythagorean theorem: l1 +l2 = d

x1²+y1²) x2²+y2²) x1 - x2)² y1 - y2)²

x1² +y1² +x2² +y2² =x1² -2x1x2 + x2² +y1² -2y1y2 + y2²

0 = 2x1x2 - 2y1y2

x1x2 + y1y2 = 0

Extended to 3D angles: x1x2 + y1y2 + z1z2 = 0, then the vectors (x1, y1, z1) and (x2, y2, z2) are perpendicular.

In summary, the sufficient and necessary condition for the perpendicularity of the two vectors l1,l2 of any dimension is that the Qing brigade: l1 l2=0 is true.

In mathematics, a vector (also known as a Euclidean vector, geometric vector, vector), a stool is a quantity with magnitude and direction. It can be visualized as a line segment with an arrow. The arrow points to:

represents the direction of the vector; Line Segment Length: Represents the size of the vector. The quantity corresponding to a vector is called a quantity (called a scalar in physics), and a quantity (or scalar) is only a magnitude and has no direction.