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Vector cross multiplication The result of multiplication by "·" is a scalar quantity; A·B=|A||B|cosW (A, B have vector scale, it is inconvenient to print out. W is the angle of two vectors). The result of multiplication by "×" is a vector perpendicular to the plane of the original vector. A×B=|A||B|sinW. Why? Vector cross multiplication The result of multiplication by "·" is a scalar quantity; A·B=|A||B|cosW (A, B have vector scale, so it is inconvenient to print out. W is the angle of two vectors). The result of multiplication by "×" is a vector perpendicular to the plane of the original vector. A×B=|A||B|sinW. Why?
The result of multiplication by "•" is a scalar; A•B=|A||B|cosW (A, B have vector scale, so it is inconvenient to print out. W is the angle of two vectors). The result of multiplication by "×" is a vector perpendicular to the plane of the original vector.
A×B=|A||B|sinW. Why? Can you prove it?
Vector product of two space vectors
Vector AB=(x1, y1, z1), Vector CD=(x2, y2, z2)
Vector AB×vector CD=(y1z2-z1y2, x2z1-x1z2, x1y2-y1x2)
A new vector is generated whose direction is perpendicular to the plane defined by vector AB, vector CD and whose direction is defined by the right-hand rule.
Geometric significance of vector product of two space vectors:
|Vector AB×vector CD|=|vector AB vector CD|* sin <向量AB,向量CD>
The module of the resulting new vector is the area of the parallelogram with vector AB and vector CD as sides
As for proof, it is easy to prove by plane geometry.
In practice, you don't have to prove it, just use it
Meaning of Vector Cross Multiplication? What can I ask? Vector a, b, c, c = a × b, which means that c is perpendicular to the plane determined by vector a, b. Meaning of Vector Cross Multiplication? What can I ask? Vector a, b, c, c = a × b, which means that c is perpendicular to the plane determined by a, b vector.
It's both geometric and physical.
I don't know what you want to know.
Geometrically, the area of a parallelogram of these two vectors
The physical meaning depends.
It's geometric and physical.
I don't know what you want to know.
Geometrically, the area of a parallelogram of these two vectors
The physical meaning depends.
On the Problem of Vector Cross Multiplication Vector BA =1/2(2 vector a + vector b-vector c) Vector BC =1/2(vector a + vector c) Vector BA-multiplication vector BC =? On the Problem of Vector Cross Multiplication Vector BA =1/2(2 vector a + vector b-vector c) Vector BC =1/2(vector a + vector c) Vector BA cross-multiplication vector BC =?
Use the formula: a×a=0, a×b=-b×a
BA×BC=1/2(2a+b-c)×1/2(a+c)
=1/4(2A×c+b×a+b×c-c×a)
=1/4(3A×c+b×a+b×c)
Vector cross multiplication problem For example, if the two vectors a (1,5), b (2,3) and the angle between the two vectors are assumed to be@, can we write out the detailed solution process of sin@? ) Vector cross multiplication problem For example, if the two vectors a (1,5), b (2,3) and the angle between the two vectors are assumed to be@, can we write the detailed solution process of sin@? ) Vector cross multiplication problem For example, if two vectors a (1,5), b (2,3) and the angle between two vectors are assumed to be@, can we write the detailed solution process of sin@(is the cross multiplication of vectors limited to three-bit coordinates? )
The following "." means dot multiplication and "X" represents cross multiplication. Solution 1: because a =(1,5), b =(2,3), a.b =17,|a|= root 26,|b|= root 13. Because =@, cos@=(a.b)/(|a||b|)=17/(root 26* root 13)=(17/26)(root 2). Because@belongs to (0, pi), sin@= root [1-(co...
How to calculate the result of vector cross multiplication with right-hand rule?
The direction of vector c is perpendicular to the plane where a and b are located, and the direction shall be judged by the "right hand rule "(the direction of vector a is represented by the four fingers of the right hand, then the fingers swing toward the direction of the palm of the hand to the direction of vector b, and the direction of the thumb is the direction of vector c).
If vector a=(a1, b1, c1), vector b=(a2, b2, c2),
So
Vector a·vector b=a1a2+b1b2+c1c2
Vector a×vector b=
|Ijk|
| A1 b1 c1|
| A2b2c2|
=(B1c2-b2c1, c1a2-a1c2, a1b2-a2b1)
(I, j, k are unit vectors of three coordinate axes perpendicular to each other in space).
Analytic geometry of space:(a, b, c are vectors, x is cross multiplication,* is point multiplication) If (axb)*c=1, then (a+b) x (b+c)*(c+a)= why is it equal to 2? Analytic geometry of space:(a, b, c are vectors, x is cross multiplication,* is point multiplication) Given (axb)*c=1, then why is (a+b) x (b+c)*(c+a)= equal to 2?
The following X denotes a cross multiplication,... denotes a dot multiplication.(a, b, c) denotes a mixed product of a, b, c, i.e.(a, b, c)=(aXb)... c.========= Since (a+b) X (b+c)=aXb+aXc+bXb+bXc=aXb+aXc+bXc,(a+b) X (b+c)...(c+a)=(aXb+aXc+bXc)...(c+a)=(a, b, c)+(a, b, a)+(a, c,...
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