The formula of the included angle between the straight line and the plane: sin0=| vector a* vector n/(] vector a vector n)=mA+nB+pC/ radical sign ((m2+n 2+p 2) (a 2+b 2+c 2)).
Among them, vector A is the direction vector of straight line L: (x-x0)/m=(y-y0)/n=(z-z0)/p, vector N is the normal vector of plane A: Ax+By+Cz+D=0, 0 is the included angle between straight line I and plane A, and the included angle between straight line and plane is defined as 0&= & lt=/2
There are actually two formulas here. The former formula can be called "line-plane included angle vector formula" and the latter formula can be called "line-plane included angle parameter formula". Let's first prove the vector formula:
As shown in the figure, it is known that point Q is the intersection of line I and plane A, 0 is the included angle between me and plane A, line POL intersects plane A at point O, and line L intersects point P, then vector PO is the normal vector of plane A. 。
If vector a= vector PQ and vector n= vector PO, then cos(90 degrees -0)=| vector a* vector n//(] vector a| vector n)), then sin0=| vector a* vector n]/(/ vector a vector n/) vector formula is proved.
Angle:
Mathematically, the minimum positive angle formed by the intersection of two straight lines (or vectors) is called the included angle between the two straight lines (or vectors), which is usually recorded as ∠ θ (included angle), and the interval range of the included angle is {θ| 0 ≤θ≤π/2}.
Basic explanation:
1. slender articles made of silk, cotton, hemp, metal, etc.
2. Geometrically, it refers to a figure formed by arbitrary movement of a point, which is long but not wide or thick. Divided into straight lines and curves.
3. Something as slender as a line.
4. Traffic routes.
5. It refers to the ideological and political line.
6. Where the edges meet.
7. Metaphor is close to a certain margin.
8. clues.
9. Used in abstract things, numerals are limited to "one".
10. Last name.