The equation of a straight line allows to define its position in space unambiguously. The straight line can be set by two points as the line of crossing of two planes, a point and a collinear vector. Depending on it it is possible to find the straight line equation in several ways.
Instruction
1. If the straight line is set by two points, find its equation on a formula (x-h1) / (h2-h1)= (at-u1) / (u2-u1)= (z-z1)/(z2-z1). Substitute coordinates of the first point (h1, u1, z1) and the second point (h2, u2, z2) in the equation and simplify expression.
2. Perhaps, points to you are set by only two coordinates, for example, (h1, u1) and (h2, u2), in that case find the equation of a straight line on the simplified formula (x-h1) / (h2-h1)= (at-u1) / (u2-u1). To make it more evident and convenient, express at through x – lead the equation to a look at =kkh +b.
3. To find the equation of the straight line which is the line of crossing of two planes work out the equations of these planes in a system and solve it. As a rule, the plane is set by expression of a look Ah + Wu + Cz+D=0. Thus, solving the system of the Ç1st + V1u + C1z+D1=0 and the Ç2nd + V2u + C2z+D2=0 concerning unknown x and at (that is you take z as the parameter or number), you receive two given equations: x =mz+a and y=nz+b.
4. If there is a need, from the given equations receive the initial equation of a straight line. For this purpose express z from each equation and equate the received expressions: (ha) / m=(y-b)/n=z/1. The vector with coordinates (m, n, 1) will be the directing vector of this straight line.
5. The straight line can be also set by a point and collinear (sonapravlenny) it a vector, in that case for search of the equation use a formula (x-h1)/m=(y-y1)/n=(z-z1)/p where (h1, u1, z1) – point coordinates, and (m, n, p) – a collinear vector.
6. To define the equation of the straight line set graphically on the plane find a point of its crossing with axes of coordinates and substitute in the equation. In case the corner of its inclination to an axis oh is known, to you will be to find a tangent of this corner (it will be coefficient before x in the equation) and a point of intersection with an axis ou enough (it will be the free member of the equation).