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Using vector method to solve Find the cosine value of the angle between the lines L1: 2x + 3Y + 1 = 0 and 2x-y + 3 = 0
The problem can be transformed into solving the cosine value of the vertical vector of two lines
On using matrix to calculate plane normal vector
It is said that there are two vectors (a, B, c) (a, B, c) in the plane
Then the following algorithm can be used
│px│
│ │=pz-xy
│yz│
Then the normal vector is (│ BC │, │ AC │, │ ab │,)
│BC│，│AC│，│AB│
I would like to know if this method is correct and if it is applicable.
The normal vectors of two vectors are obtained by their cross multiplication
http://baike.baidu.com/view/452810.htm
There is this kind of algorithm in it. It's right. It's applicable in any case, because it's a definition, just like the definition that square a is the multiplication of a and a itself
Two points:
① This statement is not quite right. It should be "using determinant to calculate plane normal vector". Determinant is a kind of operation symbol, and the final result is a number. Matrix is a mathematical object, where it exists, not an operation, just like vector can not calculate a number (in fact, vector is a special matrix with only one row or one column)
② The formula of normal vector is different from that in encyclopedia. In fact, it is the same. The first line in Encyclopedia is ijk three unit orthogonal bases, which is a third-order determinant. As long as we use the determinant expansion theorem, we can get that it is equal to
（│bc│, │ac│,│ab│,）
│BC│,│AC│,│AB│
Linear algebra in college
Should the building owner be a senior high school student, or a college student who only goes to advanced mathematics instead of linear algebra?
What are the contents of vector operation rules?
Is there only parallelogram rule? Should it be more than that?
Parallelogram rule ~ by moving the vector to build a parallelogram, the opposite side is the vector sum~
Another is orthogonal decomposition~
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