Distance from point to straight line

Distance from point to straight line: ax+by+c = 0 coordinate (Xo, Yo), then the distance from this point to this straight line is: │ AXO+BYO+C │/√ (a? +B？ )。

Distance formula from point to straight line

Line Ax+By+C=0 coordinates (Xo, Yo) So the distance from this point to this line is:

d=│AXo+BYo+C│/√(A？ +B？ )

Formula description:

The linear equation in the formula is Ax+By+C=0, and the coordinate of point P is (x0, y0).

Of all the line segments connecting a point outside the straight line with a point on the straight line, the vertical line segment is the shortest, and the length of this vertical line segment is called the distance from the point to the straight line.

Distance from space point to straight line:

What is the distance from the point m (1, 2,3) to the straight line {x+y-z = 1, 2x+z = 3}?

Z=3-2x and y=4-3x can be obtained from two planes. Therefore, the linear equation is x/(- 1)=(y-4)/3=(z-3)/2,

The direction vector of a straight line is (-1, 3,2). Let N(-t, 3t+4, 2t+3) be a point on a straight line, and the MN vector is (-t- 1, 3t+2, 2t).

If MN is perpendicular to the straight line, (-1, 3,2) * (-t-1,3t+2,2t 2t) = 0. Solvable t=- 1/2.

The modulus length sqr(6)/2 of MN is the requirement.