Let a (x 1, y 1), b (x2, y2), c (x3, y3)?
By a-> b-> c->; Turn counterclockwise. (determinant writing requirements) Let the area of a triangle be S, then S=( 1/2)* (determinant is as follows)?
|x 1 y 1 1|?
|x2 y2 1|?
|x3 y3 1|?
s =( 1/2)*(x 1 y2 * 1+x2y 3 * 1+x3y 1-x 1y 3 * 1-x2y 1 * 1)?
That is, the formula for calculating the triangle area with the coordinates of three vertices is: s = (1/2) * (x1y2+x2y3+x3y1-x1y3-x2y1-x3y2).
Mathematically, determinant is a function of matrix A whose domain is det, and its value is scalar, and it is denoted as det(A) or | A |. Whether in linear algebra, polynomial theory or calculus (such as substitution integral method), determinant, as a basic mathematical tool, has important applications.
Determinant can be regarded as a generalization of the concept of directed area or volume in general Euclidean space. In other words, in N-dimensional Euclidean space, determinant describes the influence of a linear transformation on "volume".
As shown in the figure, point A is the perpendicular of MN, and point B is the vertical foot.
then what AB=AP×sin30 = 160×0.5=80m
∵? AB=80m< 100m
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