When the modulus and direction of C are clear, the vector C can be determined.
This is a definition and a common attribute, which must be remembered.
Because vectors are directional, the product of vectors cannot follow the definition of product of numbers and needs to be redefined. The above is a definition. Our mathematics department calls it the outer product (or cross product, because it is a cross B).
The mechanical knowledge cited in the book only illustrates its physical significance. Remember, there is a definition before there is a physical meaning.
You may encounter another definition. If a and b are two vectors, define c=a? B, C is a number, and the value of C is c=/a/*/b/cosA, where A is the included angle of ab. Our math department is called inner product (or dot product, because it is point A and point B).
Its physical meaning is that when an object is acted by a force with vector A, resulting in displacement B, then C is the work done by force A to the object.
These are the two most common definitions of vector multiplication, which must be remembered.
Because of different definitions, cross product and mathematical product are very different.
Let c=a×b, if a, b and c are all numbers, when b and c(b≠0) are known, a, a=c/b can be easily found.
If a, b and c are all vectors, then if b, c(/b/≠0 and perpendicular to c) is known, a = c/b cannot be found, because the included angle a between a and b is still uncertain.
Cross product and mathematical product are also related (revised edition);
1.(a+b)×c = a×c+b×c；
a×(b+c)=a×b+a×c
2.a×b=-b×a
3.(ka)×b=k(a×b) (k is a constant)
Why is the moment perpendicular to the plane defined by force and arm?
This should start with the definition of angular velocity direction. Angular velocity is a vector, but its direction is different from that of physical quantities such as force, velocity and electric field. Because when an object rotates, the linear velocity direction of each particle may be different. If it is simply clockwise and counterclockwise, this will not work, because it is relative. The front view is clockwise and the back view is counterclockwise. Therefore, the direction of angular velocity is perpendicular to the plane of rotation and follows the right-hand rule. If there is a disk on the paper,
Now let's talk about the direction of the moment, because the role of the moment is to make the object rotate or have a tendency to rotate, so its direction should also be perpendicular to the paper and follow the right-hand rule.