The normal direction of the plane is (1, 2,3).
A straight line can be determined by the point (1,-1,-1) and the direction of the straight line.
Set a point (x, y, z) on a straight line.
Then (x-1)/2 = (y+1)/(-2) = (z+2)/3.
Extended data:
From the point of view of plane analytic geometry, a straight line on a plane is a graph represented by a binary linear equation in a plane rectangular coordinate system. To require the intersection of two straight lines, we only need to solve these two binary linear equations simultaneously. When simultaneous equations have no solution, two straight lines are parallel. When there are infinite solutions, two straight lines coincide;
When there is only one solution, two straight lines intersect at one point. Is the upward direction of an ordinary straight line the positive direction of the X axis? Angle (called the inclination angle of a straight line? ) or the tangent of the angle (called the slope of the straight line) to indicate the inclination of the straight line (for the x axis) on the plane. Slope can be used to judge whether two straight lines are parallel or perpendicular, and also to calculate their intersection angle.
The coordinates of the intersection of the straight line on the coordinate axis and the coordinate axis are called the intercept of the straight line on the coordinate axis. The position of a straight line on a plane is completely determined by its slope and intercept. In space, when two planes intersect, the intersection line is a straight line. Therefore, in the spatial rectangular coordinate system, two three-dimensional first-order equations representing the plane are simultaneous as the equations of the straight line obtained by their intersection.