The textbook content of high number vector product is not understood Here is the content: Why is the moment perpendicular to the plane defined by the force and arm Why is the vector product perpendicular to the plane determined by the original vector? What is the difference and connection between vector product and mathematical product?

The textbook content of high number vector product is not understood Here is the content: Why is the moment perpendicular to the plane defined by the force and arm Why is the vector product perpendicular to the plane determined by the original vector? What is the difference and connection between vector product and mathematical product?

This is a definition of vector product. If a and B are two vectors, C = a × B and C is a vector, the module of C / C / = / A / * / B / Sina, where a is the angle of ab. the direction is perpendicular to the plane of a and B, and forms a right-handed system. If the module and direction of C are clear, the vector C can be determined

Proof of vector of higher number (a × b) × C = (a · C) · B - (B · C) · a

The following a, B, C are vectors
Take a right-handed rectangular coordinate system, let
a=(a1,a2,a3),b=(b1,b2,b3),c=(c1,c2,c3).
Because AXB = (a2b3-a3b2, a3b1-a1b3, a1b2-a2b1)
So the first coordinate of (AXB) XC is
(a3b1-a1b3)c3-(a1b2-a2b1)c2.
On the other hand, the first coordinate of (a · C) · B - (B · C) · A is
(a1c1+a2c2+a3c3)b1-(b1c1+b2c2+b3c3)a1=(a3b1-a1b3)c3-(a1b2-a2b1)c2
Therefore, the first coordinate of the vectors on both sides of the equation is equal. Similarly, it can be proved that the other two coordinates are equal, so the equation holds

How to prove (a + b) · C = a · C + B · C (distributive law) in higher numbers

Prove by coordinate method: let a = (x1, Y1), B = (X2, Y2), C = (X3, Y3), then a + B = (x1 + X2, Y1 + Y2) then (a + b) &; C = (x1 + x2) X3 + (Y1 + Y2) Y3 and a &; C = x1x3 + y1y3, B &; C = x2x3 + Y2Y3, then a &; C + B &; C = x1x3 + y1y3 + x2y3 = (x1 + x)

How to use vector triangle
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In physics, a body in equilibrium with three forces can translate these three forces to form a closed vector triangle. According to the known forces and angles, other forces or angles can be obtained. In mathematics, the main operation is the addition and subtraction of vectors

The product of two primes is 39, and the sum of the two primes is: ()
Right now, it's urgent!
16, it seems

16
3+13=16
3*13=39

Let the equation | x ^ 2 + ax | = 4 have only three unequal real roots, and find the value of a and the corresponding three roots
Is there a problem with this problem? Is it not self contradictory to find out that X has six roots?

|X & # 178; + ax | = 4  X & # 178; + AX = 4 or X & # 178; + AX = - 4, that is, X & # 178; + ax - 4 = 0 or X & # 178; + ax + 4 = 0  there are only three unequal real roots, and the △ of X &  178; + ax-4 = 0 is always greater than zero  (?) = A & # 178; - 16 = 0  a = ± 4 when a

Y '= 4 / X & # 178; ≥ 0 why?

Wrong, it can't be equal to zero, because the square of X is greater than zero,

What is (3AB & # 178;), # 178; + (- 4AB & # 179;) · (- AB) after simplification

（3ab²）²﹢（-4ab³）·（-ab）
=9a^2b^4+4a^2b^4
=13a^2b^4
Do not understand can ask, help please adopt, thank you!

Read the following process: solve the equation: | 5x | = 2
(1) When 5x ≥ 0, the original equation can be reduced to a linear equation of one variable, where 5x = 2, and the solution is x = 25;
(2) When 5x ＜ 0, the original equation can be reduced to a linear equation of one variable - 5x = 2, and the solution is x = - 25
Please follow the example above to solve the equation 3 | X-1 | - 2 = 10

(1) When X-1 is greater than or equal to 0, the original equation can be reduced to a linear equation of one variable 3x-5 = 10, and the solution is x = 5;
(2) When X-1 ＜ 0, the original equation can be reduced to a linear equation of one variable - 3x + 1 = 10, and the solution is x = - 3

Let a be a nonzero matrix of order n and | a | = 0. It is proved that there exists a nonzero matrix B of order n such that ab = 0 (using the knowledge of determinant)
We don't need the knowledge of matrix rank, we only need the knowledge of matrix and determinant or equations

Certification:
|A | = 0 means AX = 0 has nonzero solution
Then, if X1 is the solution vector of AX = 0, then we can use X1 to form the solution matrix B
B=（x1,x2,… , xn), where X1 is not equal to 0, X2 = X3 = =xn=0
And B is a non-zero matrix, that is to say, B is the matrix